Data analysis assignment 1 Stata

in this video I'll explain how to do the First Data analys assignment of my quantitative analysis course or quantitive research method scores using STA and uh sta is one of the two statistical software that I use for my empirical work I also use R but sta is a bit more user friendly compared to R so if I have to do an analysis then sta is typically my default Choice the assignment here on the course website you can access it using uh guest access so if you know the course code you can just type into the my courses alter fi search and view the assignment uh it is to use the prestige data set so this data set is uh data on occupations and their incomes and education levels from the Canadian census from the 1970s it's from John Fox's applied regression analysis book and uh this is the uh the command for loading the data so I'm going to load the data first and just to get some some data into STA and then I'll I'll show what the STA user interface is about so the overall plan is the first uh walk you through what data looks like and then uh go through and and show how you actually do the analysis we'll first explore the data a bit then we run some regressions we do some Diagnostics and then we export the results and finally produce a report using exported results so I'm going to paste the command here and it loads the data if you find it problematic to load the data for example if you get an error then uh something that has happened over the past is that uh the UCL website will reload the data they change the location of the data so if they change the uh the structure then this link might be broken if you are looking at this or watching the screencast later and uh it doesn't work for you please check the correct link on the course website all right now uh what is US sta about and uh this is data with with factory settings so so this is just just three STA and uh we can see here that we have three panels so panel one here main panel and panel um three here uh your sta might look different so if you're using sta on a laptop screen then uh that might be showing on sidebar layout which means that you only get this um this one side barar instead of two side bars but most people who analyze their data are probably using the wide screen so I'm going to use the wide screen because that's what you would use on a big monitor but if you are on a laptop then uh you can use the the one panel layout instead of the wide screen so what do we have here this is the uh the results window so you can see the name of the window here and uh everything that we do all the analysis results everything that data uh produces comes here so regression tables correlations error messages uh messages that data we modified comes here and then we have the command window here the command window is something that the professional researcher uses a lot so we can just type something here types data commands and then data will execute them for us so for example we can ask sta to display 1 + one so it's going to be too so you can use data as a calculator why professional researchers uh use the command is that the window to type is that it's lot faster to type commands like regress and Analysis that type type the variables instead of using State through the other way which is the menu so we can use our statistics menu here linear M related linear regression and then uh we have this D this dialogue we we click through all the tabs that we want and then we run the analysis so just typing the name of the command is often a lot faster if you know the names of the commands but if you don't know the names of the commands if you're just getting started then using the menus is probably a better option for you I'll be using the menus throughout this screencast to show how sta works then a third way to use sta is uh to do something called a do file so we can open a do file editor here and the do file editor would contain a sequence of commands and then sta will execute those commands sequentially getting to talking about commands brings us to something that differentiates statistical software from Excel so if you analyze data with Excel you are usually uh looking at something like like this so you have the data shown on on a a sheet with rows and columns we can see that in sta as well and then you would uh do your analysis here you could for example click on a cell and then just type something here and calculate an average for example so you your analysis and your data live in the same file in an Excel statistical software doesn't work that way so stat in statistical software the data are what they are they are in a file and the data file should never be edited for example we can't even edit this here so it's it's all read only how we uh manipulate the data how we analyze the data is that we execute a series of commands for example we might first execute a command for calculating means of the variables we might look at the means then we might notify that there's a data entry error we might execute a command to fix that error then we can we could run a command for regon analysis and then a command for ex exporting the regron results to a Word document so instead of thinking about the data and Analysis as cells you have an analysis file that contains all the commands that produce the analysis result that you want and then you have the data file that is the starting point all right now let's take a look at uh once we know how to use data so there's the command there is the uh the statistics and then there is the uh the do file editor we can where we can type many different commands uh on the left we have history so the history tab shows us all the commands that we have run this far so if you want to know how to uh produce the results that you just got the history shows you that these were the commands that you run uh we can also uh see uh how the history reacts when we do errors so let's let's type display and let's do a typo that produces an error and uh we can see red here it shows that this was an error so whenever we want to uh when if we ever want to rerun this analysis again we would know that we should not run this line in red which is uh an error then on the right hand side we have um the variables panel and then there's a project browser if you are working in a bigger project project manager I don't use project manager but some people like it uh we have variables so the variables are here so if we want to calculate the uh the mean of the variable we would do for example sum sum which is sort for summarize and then we we can type the name of the variable of the best and title it gives us uh uh the the mean but that's that's uh that's a bad example because that's a string variable so we can do we can calculate the mean of the variable uh income so sum income and uh so we we refer to the variables by name and then this label is a more descriptive name it tells us what that variable is about and if you ex do figures or if you export tables they always uh use the label so if you are someone who reads an analysis result from an art from a a journal article for example you want to see uh the variables explained like a type of occupation instead of _ type which doesn't really tell anyone who is not working with this data what that is about so the variable name is something that we use to refer to the variable and then the label is a more like a descriptive name of the variable and we have properties of the variable so when we pick a variable here we can see that this is a string variable so uh the string variable means that it is text and a text variables can be analyzed statistically like uh I tried to create a summary calculate mean standard deviation minimum or maximum of that variable um you can do that mean doesn't exist for text um then uh we have education here so it's it's float float means that it's decimal number and then we have occupation type here bite bite means that it's a small whole number so small integer and it also has a label here so occupation tab is a labeled numerical variable then up here we have a log file viewer I don't normally use the log files because um when I run an analysis I always store the commands into a do file and if I want to recreate what I see here I'll just rerun the do file but if you want to for some reason save your your log like you would do in this assignment at the end then uh you can do it from the user interface here so there's um this big append view various logging options viewer is to help youer you can also uh type here for search that will give you help and uh graph if we have Graphics open we can we can look at the graphics Windows here the doile editor opens the doile editor where we can specify sequence of commands I'll show that at the end of the video and then we have data editor and data browser you should pretty much never use the data editor unless you are generating like a small example data for yourself or or typing in a data set that you have gotten in a non- electronic format which is uh which you might get for example if you have uh paper based surveys then you might type them in uh data should never be edited directly because if we uh change something here so for example if we change the uh the income of the government administrators administrators to be one then uh it doesn't really document what was done so it just test that uh income was replaced to be one in observation number one that's not very descriptive so it doesn't tell us like why did we choose that variable and why did we pick a value num one it's much better to to do any changes using commands so I'm just going to reload the data generally uh you shouldn't use the data editor if you want to eyeball the data then you can use the the data browser so the data browser is the same as data editor except that this is read only so we can't edit anything we try it doesn't allow us to edit the data browser shows us that we have uh three different kinds of variables we have red we have black and we have blue so the red indicates that it is a text variable so we can see the this is a value it's government administrators and it's text black is normal numerical variable and then this blue is uh labeled categorical variable so it's it's a numerical variable with labels so uh it's it's this professional for example has a value of three but it's going to be shown with the label in the in the output the reason for that is that in categorical variables the actual numbers so we have numbers from 1 to four corresponding professional blue color white color and unknown occupation types it doesn't really matter so we can say that if unknown is is uh one and uh blue color is four then blue color color is is four times unknown it doesn't make any sense so these are just codes and and the numbers don't make any any uh make a difference we could recode them with with different numbers and the analysis for the conclusions it wouldn't wouldn't matter so uh for that reason we are always printing these uh categorical variables with the label instead of the the numerical value because the value again is arbitrary all right then we have a couple of buttons we have the more button here and uh the more button what it does I'm just going to use I'm going to switch the menus in a minute but I'm going to show a few few features one annoying feature of sta is that when you start the first time with the default settings it only prints you uh one screen's worth of of output and then it says more is coming and uh it stops and we can click there or we can click on the more button and then you can view the rest of the output I don't like that feature and I don't know any uh professional researcher who would use that feature maybe someone does and it's a lot easier to just uh scroll back back if I want to see the output little by little instead of uh of typing more the only use where you might have for more is that your your output is is uh so large that it doesn't fit into the uh this data results window then uh you might find some some usefulness from the more option but uh you can just increase uh how many lines of results this uh results window shows and and it can be pretty large so it's uh if you change the settings then that eliminates a need for more so whenever I start analyzing anything with sta what I do uh is change a few settings and I recommend that you do this uh setting changes yourself as well so we do set more of comma permanently and the permanently means that it's going to be stored in our preferences and uh when we restart sta then we don't need to do set more of anymore if we do without the per without the permanently option then the preference is stored only for this session and the more option is going to be on again when we restart data so uh we do that another uh feature that sta has is variable abbreviations so for example if we type some I then uh it shows us the Val the summary of income you so you can uh you can uh do these abbreviations if we do uh let's do describe O then it says that o could mean two different things so it's either a occupation code or occupation type so uh I turn this off and the reason why I turn this abbreviations of is that is is twofold first of all I think uh if you always typee the full variable name then it produces more readable uh statea code for someone else to interpret and it also avoids errors so uh before I when I used to have this abbreviation feature on then uh I might have inadvertently analyzed an incorrect variable because I had uh just type a few letters from the beginning of the variable and when I have variable names that are very similar it it's very easy to analyze incorrectly analyze an incorrect variable so we're going to turn that off as well so the set setting name is set bar up R of comma permanently and um now you can probably start to see a pattern that statea commands is always a command then there is a main specification and then there is an option so the options are something that kind of like uh make give additional information for sta on what this sta should be doing all right and now if we can do some I it tells that the variable I is not found because it doesn't do abbreviation anymore so when I get do something uh then uh with a new set of sta or new install of sta I always set the more off and VAR abbreviations off because I think it makes it working with data bit less error prone and more pleasant all right then another preference that you might want to change is changing the font size so if I present in a class then uh I I you just right click somewhere preferences and uh you can increase the phone size I tend to have 10 when I analyze data on my computer but this is set to 15 for the screencast and then uh uh the command window is set to 15 and I think that's good for the screencast but if I analyze data myself I would have 10 just to have more information shown on the screen all right now let's get to the analysis and uh what we need to do first is to explore the data and um the data exploration typically starts by by doing univariate statistics so uh we have here the statistics menu and data menu these are contain various different uh expression commands and I don't use this very often so I might need to look for a command a bit but describ data we can do a describ data in memory or in a file all right so that tells us something and uh when you do a command from the menus then you get this kind of dialogue and the dialogue um asks us what to do so uh we want to describe data in memory we leave it empty so we want to have description of all the variables and not just the subset and uh then various options and typically the defaults at least on a very basic level are going to be uh useful for you so so you don't need to change any of these unless you are specifically need to in which case you would know the need so we're going to describe and that shows us a description of uh the data so this description is pretty much the same thing that you would have uh have here in the properties and in the labels here so we can see uh we have one text variable we have one decimal number one whole number decimal number decimal number whole number and then a small whole number with a valuable label value label which tells us that this is a categorical variable so whenever you start with a new data set I I typically print the this describing just to show what these data are about it's lot faster for me to uh to show look at this then it's to look at the um the the right panel and in fact when I use use data I typically don't have these panels open so uh the command history I can open if if I need it I really do need it because I work with a do file and the do file shows all the sequence of commands that I've done and then I tend to remember my data so I don't need to have the variable's name here if we want to um then uh do something for for uh individual variables like we can see the command is described if we want to com describe an individual variable we can either type the command or we could uh redo the menus and then we can we can type this click on these variables here and then uh press enter so we can construct the command by by typing the name of the command or and then clicking on the variables if we want to redo the command rerun the command again we can use a page up and page up Scrolls through or goes to the the command history so we can go uh page up and page up now we can kind of revisit what we done in the past or if you want to redo something then you can just uh rerun the command all right another useful command in the uh in this data in the data window or data menu is inspect variables so um inspect variables uh empty for all we're going to inspect them so this gives us something about like more descriptive statistics and uh you can U use wild cards here so if we want to uh only uh do everything that starts with OC we could do OC star and uh that's actually a useful because it it shows how the descriptive or the inspection works for uh a a string variable see there's like uh no no observations here no numerical observations so everything is missing it's just text no numbers and then we have the occupation code here and then we have uh occupation type so this is the categorical occupation code it's just a code it doesn't really uh plus anything then we have uh a third way of describing the data so uh something that professional researchers sometimes use is that if we have many people who work using the same data set or the data set is something that you've collected uh for someone else to use then you produce something called a code book and the code book explains what the data are it tells the variable names it tells the the labels it tells the uh the data types like is it text or is it uh numbers is it uh whole numbers is decimal numbers and then provide some descriptive statistics so we can do our data and uh then there is the uh the code book and I will have to look for it it's in uh describe data yeah describe data contents codebook so this is another way of showing the data and it's a bit more more uh like verbos way so it shows us uh statistics uh for string variables it shows us examples so we can see examples of what kind of things this variable has so we can see that these are all all caps there no spaces but underscores and the longest one is 25 characters uh then we have this education we can see that it uh has 96 unique values mean standard deviation then this tells us about the distribution so it's 10% is 7.52 so 10% are less than that and then uh 90% are less than 14.17 so uh the number of Education uh the years of education is pretty small compared to current standards then there's the income uh percentage Prestige and uh occupation type now we can see this is useful information because uh this is a categorical variable it it shows us a bit different it doesn't show us means because a mean of a categoric variable doesn't really tell us anything rather it shows that we have we have four uh unknown equations with unknown category and this is uh the VA the value for unknown is one the label is question mark then we have 45 blue colors that are CED at two are 30 professional occupations or 23 are white color occupations so and there's no missing data so everything um all 102 observations always have data for every variable so that is the uh the Third Way of or fourth way of of uh of looking at the the data and um or third way then the fourth way is through the statistics so we have summaries and summary Des statistics summary statistics so this is the uh this is kind the thing that I use the most and uh summary statistics uh let's let's do additional statistics just to show what it looks like it tells us basic descriptive statistics of each variable so um we can see that it added the option detail if we run without that option then we just get means standard deviations minimums and maximums so I use both of these and uh when you do univariate analysis you want to understand what is the range of the variable like what is the minimum maximum what what is the mean we can see here that the uh for income the mean is uh 6,700 maximum is 25,000 and minimum is 600 so it tells us that the data are skewed because the distance from the minimum to the mean is 6,000 and the distance from the minimum uh from the mean to the maximum is is about close to 20,000 so the data are skewed so that there are very few patients with very high incomes but a lot more occupation with lower levels of incomes then standard deviation tells us about the variation of the r data and then uh this generally tells you about what is the unit and U it's useful for regression interpretation occupation type mean and standard division doesn't make any sense because it's a category but we can see that there's there are four four elements of four different uh distinct values or we can guess that there are four distinct values Val in this category all right that is uh the basic uh description of the data and then another thing that we would often want to do is to do uh look at the distribution slow so uh if you think about a distribution you might think about a normal distribution which looks like a bell curve so it goes up and then there is kind of peak and then it goes and then it it flattens like that so that shows where the observations are located that's a useful display and we can use do that with sta so there are a couple different ways of of um doing um distributions we can do our statistics and then there is uh distribution plots and tests and uh these are various ways of characterizing or describing the distribution of a variable uh stem LIF display is is one of um my my favorite ones and the reason is that it's it's uh it doesn't produce a graph but it produces uh the graphic as text so it doesn't open a new graphics window but it just puts the results into the results window and we pick one variable so we pick income in practice uh when you analyze your data you would look at the distribution of every variable and you might use the plots or some other plots for that so I'm just going to um do that and it shows us the distribution so if you look at this it's kind of like a normal distribution flipped 90° so uh this shows us the first two numbers so let's it's easier to uh the first two digits so it's EAS to look at this uh instead of the small ones so the largest value in the data is 25,000 and then these stars are filled in with whatever value value is here so the largest value is is 2,879 so everything uh separated by comma means that it's a separate observations so we have two observations in the 25,000 range and they are 25,38 2,879 here we have two observations with 0, thousands so 6111 and 918 those are the smallest observations and you can see that the peak of the data is roughly around 5,000 so that might the median might be somewhere here 5,000 or 4,000 somewhere here and um so this is the stemma LIF plot then and another useful way of looking at the data is to look at uh the the kernel density plots yeah we can find Graphics distributional graphs and uh then there is uh density C density estimation so this is uh what I would I would often use and we're going to take a look at income and uh just leave everything as default and uh that statea Graphics is a bit slow but that shows us the um the distribution graphically so the height of the line tells how many observations we have have here so we have two observation with 25,000 here and most are here so it kind of like looks like a normal distribution with a long tail so it's it's skewed to the right and um we can also uh do the same graphic with um with options so if we want to analyze if the variable is normally distributed then uh we can go and look at these different options so I'm going to so if in this would be for selecting observations we can choose based on on a a condition or we can use a range of observations uh we could use survey weights if we want to weight some data more than others I never use it myself but this is the uh this is how we plot it and then we have our additional density plots we add normal density plot and uh that gives us a reference so it gives us the the normal distribution that best describes this data and we can see that the data are not normal they are they are more skewed than what the normal distribution would exist so if you want to analyze if something is normally distributed uh this graphical way of using kernel density is the way to go and um so you can you can do that also type in K density let's do uh education tab autocompletes the variable name and then that shows us the other the current density of Education when you analyze a data data set then uh you would use these uh two commands you can pick either the cority plot or the stem and leave plot or you can do both um but that's they they tell you the same information in different ways uh you would do this for for every numerical variable except those that are categorical so every continuous and every U every variable that has a numerical interpretation instead of a categorical interpretation you would do this and then look at the distributions just to understand like do I have any extreme values and and how the data look like it's very important that you understand your data when you start analyzing so that is the um the um distribution and uh of the University analysis then uh what we need to do next is to to look at uh multi varat analysis so so and we start by looking at by variat analysis and because the the point here is to do a a regression analysis uh regression is a linear model so we want to understand the linear dependencies in the data and uh correlation Matrix is the uh the way to understand linear dependency so we want to do correlations next moving to to byar relationsships so we do statistics and uh then um you can you can guess where it is but I'll just type the name of the correlation so there is a it is summary and descriptive statistics so statistics summary and descriptive statistics and then uh statistics summary this is the statistics and then are correlations and Co variances we we click all variables and we click okay and uhu now we have a a warning from sta that occupation title is ignored because string variable in some older versions of sta if you uh try to correlate a text variable it produces an error and sometimes uh if you try to do a for example a a ression analysis with a string variable it might produce an error but now sta is Mark and it drops the occupation type from uh from the data the occupation code is just a categorical code and it doesn't really tell us anything uh if you really want to understand what it is it's like a sensus code you can find the documentation of the Canadian sensus and see what the different codes actually how they're defined but it's not going to be a useful exercise for you I guarantee all right so this is a way and of looking at the data in a byari way and if you think about a a published paper this would be the table one descriptive statistics and correlations this would be the correlations part then we have uh correlations here how we would interpret we would say check if the correlations make sense like if there's a large correlation this 0.57 is pretty large so in social sciences correlation of 0.3 is something that we would consider meaningful definitely 0.5 0.6 definitely very large correlation so there be a large correlation between education and income and even larger between education and Prestige and um then there is a large between presti and uh income makes a lot of sense if you have prestigious occupation is probably uh earning you more money and then uh we have share of women women might be are discriminated against so the income here is uh negatively correlated with Z of women and uh that's also understandable at in in 1970s so that is the correlation you would go through uh all the correlations and and look at what are the large ones do they make sense are there some correlations that are small like non-existent do they make sense for example uh we might take a look at education and it doesn't uh seem to be correlated with share women that kind of resonates with our everyday understanding that both men and women tend to get education at about the same same rate so there's a small positive correlation but that's very small and the data are pretty small one observations only so this is one way to understand the by variate our relationships another way is to is to look at scatterplot Matrix so we do scatter and uh then it's in graphics and uh two-way scatter block Matrix yeah Graphics scatter Matrix so um I'm not going to talk about all these Graphics I'll just show the ones that are you are needed for for this assignment and um we have um we start with all the variables okay and uh okay we have to specify them we click education we click income we click percentage Movement we click uh Prestige and uh occupation code is just the sensus code it doesn't tell us anything and then occupation type uh that's categorical it doesn't really tell us much but let's still include it just to show what it looks like and um we click okay and that shows us a graphical way of uh graphical representation of the correlation matrics let's make it a bit bigger now we can see that uh this is always the the the um the x-axis on the top and then on the right or left hand side is the income so we can see that education is the x-axis here uh income is the y- AIS here and uh the relationship seems to be increasing so we can take a look at the shape of the relationship correlation test tell us that there is a Rel relationship so this correlation but 0.5 income and education 0.56 and this plot shows us what is the shape of the relationship so this is not a linear relationship so the income doesn't increase linearly with our education but rather it looks more like an exponential so first there is very little increase in income and then U at about 10 years or something like that it starts to go up quite rapidly and that also um makes a lot of sense because uh if you think about how Education Works is that for the basic education which is now 9 years mandatory in Finland and then you have either high school or occupational um vocational school then the first nine years basically give you just uh the understanding of how to be a citizen and then uh but it doesn't give you any professional qualifications so only after the basic education you start to get some professional qualifications and if you really want to get uh to a high paying occupation then typically it requires a University degree so you get a lot more uh additional income from a University degree than you would get for a high school degree so that's why it's it's nonlinear then we have one outlier here so this I know the data so this is general managers and um we can print the uh the observation names here but it doesn't really make sense for for this plot because there is so much going on uh we can see that uh education here and and share of women it doesn't correlate there's like no no clear pattern here there is uh a clear linear relationship between a prestige of an occupation and income uh we can see a bit of uh we would call it heteroscedasticity so these are more spread out over here than they are over here so these are some of the things that you can take a look at in this figure then we can see from the occupation type so um the occupation types are here one that's the unknown two three and four we can see that there are the category number three is clearly distinct from the others this is not an ideal uh plot for inspecting the difference between the category variables but you can do so so you would be looking at this plot and and looking for patterns in the data and uh these are just the mirror images of each other so this is uh that's the journal managers they and that's general managers and uh these are the low um occupation low education occupations these are the low income low education occupations so uh this is just depending on which one you you want to think of as the the dependent variable if we want to think of the income as the dependent variable then uh like we do in this assignment then we will be looking at this row and uh then the Y AIS is always the income and then whatever is the other variable like occupation press uh share of women and education is this the x-axis so this is the second um byari descriptive statistics plot that I want that I a by variate descriptive analysis tool that I like to use the next thing after data exploration is to do the regression analysis so the task was to explain the income variable with the other variables and we're going to start by running one regress model the overall workflow here is to go and run the first regural model then do diagnostics for that model fix the biggest problem then run the second model do diagnostics for that fix the biggest problem and so on so what the problems are I'll get to that but the point is that you uh do a few different models where your model evolves and then you explain your thinking in that and your interpretation of results in that assignment so we do our regression by look taking statistics linear mod related linear regression analysis and there's quite a lot of U there's a few tabs here I'll explain a bit what these do in a moment but first we need to pick the dependent variable for regression analysis and we'll pick income and then we pick the independent variables we'll have education we have percentage woman we have Prestige and then um occupation code is something it's like a sensus code it doesn't matter an occupation type is a categorical variable we are not going to use the categorical variable in this assignment if you want to use it then uh you need to put i period in front of it to tell this sta that uh it's a categorical variable that needs to be dcoded but I'll take it out for now uh then there is uh additional features about the model and this is typically you don't need any of this then the other tabs here is by if and in by means that you're repeating the analysis by subgroups if you want to for example analyze the regression for each occupation group you can do so then if allows you to constrain which observations you apply for uh the regression to so for example you can apply regression only to those observations with at least 1,000 income and observation range is useful if you want to turn like quick analysis but your data is very large so you can limit the number of observations that you use weights this is for uh survey weights so if you have uh a survey design that is stratified which means that uh individuals don't have equal chances of being included but for example some uh smaller cities are overweighted compared to for example helsink if you do a survey of finish population just that we have enough uh informance from those cities then we would use these weights to accommodate that kind of sampling scheme uh this is an important one standard errors you can pick various different kinds of standard errors uh robust and cluster robots robust are something that you would uh you would use robust is for dealing with h elasticity and cluster robust is for dealing with non-independence of observation so these are very commonly used and uh then reporting there's all kinds of uh additional reporting options that you can use use uh you can pick which confidence interval you choose standardized coefficient you pretty much never use this and uh then uh in some models uh exponen in the coefficients Mak sense but it doesn't really make sense in regression analysis and then um you can you can choose what to report then there's some additional options so there's lots of options in each of these commands but typically just filling the first tab is sufficient for most purposes then then uh submit runs it right away so if we want to run multiple models we can submit and then if we want to run another model for example take one of those Parables out we submit again so submit runs the analysis without closing the tab and um okay runs the analysis and closing the closes the window like so all right now we have regr and results here and I'll cover the interpretation of these results more in on the course but we can see here that one unit increase of Education leads to uh approximately uh 177 U dollar increase in annual salary uh but it's not statistically significant so here's the P value this is the confence interval and this is the T statistic uh that is used to calculate this P value and you might wonder why educ education doesn't pay off and uh maybe it's uh a a mediation effect so that education unlocks access to more more prestigious occupations and uh then Prestige is actually what makes the difference so that you would interpret this to mean that if you take get more education but you go don't go for more prestigious occupations then uh education doesn't really pay off and personent woman is uh has a fairly strong effect so for each percentage point this variable is coded from 0 to 100 they are amount of income decreases by minus 50 so if we have an occupation with 0% women an occupation with 100% women the difference is $5,000 Canadian dollars that's a very substantial difference if you consider that the average income is like 6,000 some so these are statistically significant and this is not then we have other statistics here you should take a look at the R square and the R square tells how much the model explains the data in in management 20% 30% is very high number but because this is um sociology and the weight formation depends fairly straightforwardly on The Prestige and occupation this is a very large R square this P value is the P value of the F test so the F test test and I'll thesis that uh the R square is zero and then we have adjusted R square which is a bit better for interpretation the actual R square if your sample size is small so R square is always biased positively and adjusted R square adjust for that bias it's not fully unbiased but it tends to be less biased than the R square okay now that we have a regron analysis uh run we can do Post estimation and uh in the statistics menu there's this post estimation dialogue so post estimation refers to it means uh all the tasks that one could do after estimating model so when we click post estimation there are various different options so it's a pretty small window here or the font size is small and it can be increased uh manage estimation results this is useful for for tabulating the results so uh we but first we need to store estimates in memory so whenever you run estimates then uh those estimates will be in memory and you can apply for example various Diagnostics plots but if we want to return to the estimates later for example if you want to tabulate two sets of estimates side by side we need to save them so sta by default when you uh run a regress on any other estimation command it stores the most recent estimat in memory so unless we save the estimates then if we can only tabulate the most recent ones so whenever we run a regression analysis when we run it the next time the always the latest results override the current results unless we save them so we're going to store the estimates so we're going to estimate store we're going to call this M1 and okay once we know that uh these results are something that we we will be using then I recommend always storing the estimates but if it's just explor the data then storing the estimates is not necessary uh you can see list estimates stored in memory and um you can launch it and list all stored estimation results it shows that we have uh one stored there's income is dependent variable four independent variables or three independent variables and the intercept and then it's it's a linear regression analysis all right let's go back can do Post estimations so we need to understand uh do diagnostics after estimation always to understand whether the model explains the data well or not and if there's something that we can we can do about the results so let's go to post estimation again and uh then uh we have Diagnostics and analytics plots and there are a few important interesting plots residual versus fit the plot addable plot and then I also use leverage ver res squared plot to identify outliers these others can be used as well but this is the combination that I use res versus fited are add a variable plot and then leverage versus residual so uh let's do uh resid versus fit BL and um it runs it produce the plot in a different window and um this plot shows us that this is the Val value that the model predicts so it's the it's the prediction based on the rec equation the fitted value and this is the residual it's the difference between the fitted value and the predicted value ideally this would be a band so that there are they would all be on average at zero irrespectively of which part of the data we look at and then uh they should be distributed approximately equally around the the zero line which is the the homos cadas assumption we can see at least a couple of problems here first of all we can see that uh this is not exactly linear so if this was linear then we would have all the observations uh at uh around the zero line on average but for small observations here they tend to be above zero and for large values of fitted value they tend to be also about this uh zero line and that tells us that the effect might be curv linear so it might be that it's not linear but it's rather kind of like curving up a bit like the relationship in comparison to regression line another thing that we can see is that they are the variance of the residuals is a lot greater here than it's on the left hand side and this is evidence of het heteroscedasticity or non constant variance of the error to so these are the two things that we can take a look at in this plot we can of course identify individual observations that are distin like that is uh the general managers and it's an outlier but this is not the idea plot for for looking at that kind of things if we want to save the plot then we need to rename it and uh we can call it rvf for example r F residual versus fitted and then it's going to be saved and uh unless if we don't save a plot or name a plot then uh redoing the plot or doing the next plot will overwrite the previous plot so um I'm just going to close it because we don't we don't need this plot the second plot that we I want to show is the added variable plot and um particularly all added variable plots in one graph and the ad develop plot is useful for look for identifying nonlinearity and heteroscedasticity one independent variable at a time so I'm going to take all variables click okay and it runs it produces a matrix of plots and what these plots tell us uh they tell us what is the unique effect of education on income what is the unique defect of prestige on income what is the unique defect of prestige on income and this would be useful for identifying if one of the independent variables specifically has a nonlinear relationship with the dependent variable and also identifying heteroskedasticity so this this plots don't show a nonlinear problem as well as the previous plot but this is an additional set of Diagnostics that you can do then we have the um leverage versus res squared plot and this is U useful for identifying outliers so Leverage is a measure of influence so how much an observation influences the regression results and then uh if an observation has a large residual and large influence then it's an influence of observation and potential outlier so uh we can see that here's a potential outlier this is a potential outlier and this is a potential outlier but outliers are not something that we dropped based on just statistics we need to understand what these observations are and if they are clearly distinct and uh to know what these observations are I'm going to close the plot and then I'm going to launch it again and then there are plot options and we can choose marker properties and uh add labels to markers so we we Mark label and we have the occupation Title Here we we accept and we click okay and that shows us that we have an outlier news voice which has a large influence small residual Physicians bit of both and then general manager with a large residual all right so these are the plots that you will you should use for Diagnostics then there is a another kind of plot that researchers sometimes report and or inspect but it's not very useful which is inspecting the distribution of the residuals predictions and um predictions and the standard leverage statistics distance statistics ITC we're going to launch and prediction means that it's something calculated based on the model and we are going to calculate the linear predictions gives you the fitted values we are going to calculate the residuals and um we're going to call it R1 or rest one because it's from the first model so residual from model one and if we want to inspect the distribution of the residual we can do a uh Graphics distributional graphs and we can do for example normal quantal plot which is useful for inspecting normality so uh if the data are normally distributed then they should be on this line but because these are about the line it tells us that uh these there's a tail some observations some residual are larger than what normal distribution predicts and then there's this observation here that is a lot smaller than what the normal distribution predicts if you want to see it uh in another way you can have smoothing and densities current density estimation pick um residual then we have density plot add normal plot okay and that shows us the red is uh the normal distribution that best fits this data and then uh blue is the empirical distribution of the dat dat so we can see that the data are a lot more peaked there are more observations on zero and longer tales on both ends though more on the negative end than what normal distribution would predict so this shows that the residuals are not normally distributed that's not a problem in recursion analysis even though a lot of researchers think that it's a problem so what do we do we had uh evidence of of nonlinearity we had potential outliers then we had uh hter scity we need to fix the biggest problem first and uh the biggest problem would be the nonlinearity and we can model exponential relationships which are very common in nonlinear models very common way of modeling nonlinearity by taking a log of the dependent variable and that would make a lot of sense because then it converts the regression coefficients to relative quantities so instead of thinking about increasing your income by uh a certain amount of Canadian dollars you increase the income as a percentage relative to the current income so we're going to do log transformation of the dependent variable and create a new variable and then run the regression again so we're going to do data and then we're going to do uh create variables create new variable and the variable name name is going to be Ln income so I'm going to call it Ln let's have it underscore because that is the convention that we use in this data and then we can either create the expression or we can just type log income so log is the natural logarithm you can you can create here and then there's all kinds of functions if you don't remember the functions so we can have for example our mathematical functions here and this is the list of functions so so we can find the uh the log natural logarithm log and then uh x with type income there so that would be a way of using the the expression editor but it's easier to just type log income and then we're just going to okay and now you can see that it doesn't have a a label and we could label the data but yeah we're not going to do it for this assignment the next thing uh we do is we run a new recordon analysis there are a couple different ways to do it we can either uh just go here go to linear motion related linear recron analysis and then we can pick the um the Len income as the dependent varable click okay another option would be to just go back to the regression scrolling back the commands and then just changing the name of the dependent variable by editing it so both are pretty easy so yeah Len under score now we can see that um the effects are fairly different so um this is relative effect it means that for every uh additional percentage point of women the income decreases by about minus 1% so it's a relative effect compared to it's not no longer absolute effect and U then your task and the assignment would continue from here with the Diagnostics I will not do the Diagnostics I'll leave some for you to do so you need to go through the Diagnostics interpret the results and then choose which observations are potential outliers I will now show how you drop a potential outlier from the data so let's assume that um that we we go to the data editor data browser and we can look at observations with uh with larger residuals so we're going to sort the data data sort and then we're going to sort by res so let's assume that minister is an outlier because it has a large residual and the substantive reason for dropping mins would be that minister in this case priest is something that you don't do for money and it might also be a part CL occupation if you only work for weekend so how uh Church works in the Americas is quite different from how it works in for example Finland where I'm from so we might say that this is not a full-time profession so we'll drop it and um now we sorted the data so we could just say drop in one but it's much better to drop based on the occupation title so we can um we can copy that value from there and uh then we go to data we can can do a Creator change data and drop or keep observations so we drop and then the uh expression we can use the Expression Builder by using the create here but it's just easier to type so o tile equals so equals is two equal signs one equal sign is assignment two equal signs is comparison and then uh because it is um a string it must be in double quotes and then I'm going to drop it and then I can I can rerun the regress analysis as see what the results are like so and then I will store the estimates I can either go to the menus or I can see here that the command for storing the estimates is estimat store so we can just type estimates store M2 and now we can go go and and view here all the estimates we can either go and and see the post estimation menu here post estimation manage estimation results list estimates stored in memory and all estimates or I can just do estimates here now I dropped one observation and I transform the dependent variable to be log and the reason for doing this in one one one step is just to show show these things that you need to do in the assignment but in the assignment you need to do the sequences so if you decide that nonlinearity is the biggest problem then you need to run the model again with the log transfer dependent variable du to Diagnostics and then determine if any of the observations are outliers for example when you log transform the dependent variable then uh which observations or outliers differ so it's not a good idea to drop based on the original model but you drop from the subsequent models but just not to give you the the full answer to the assignment I didn't want AG go then we have a few things that we can we can do we might want to uh tabulate these models so there are a couple different ways post estimation gives you uh then uh table of estimation results so this is a Weck and dirty table and I'm going to say M1 M2 so this uh gives us two model side by side and if we want to add things there we can do statistics uh post estimation menus post estimation table of estimation results other statistics to be displayed and uh other statistics from E how do you know what this from E stands for well it it stands for um the whatever are the estimation results and we can do help regress so that's the help for regression analysis and you can go to the PDF menu here a PDF documentation it explains you uh the in detail what reron anal does in data this is kind of like a quick reference this is the detailed explanation it's a very comprehensive documentation and uh but now we just want to know what other statistics beyond the estimates the recursion command returns and we can scroll down here and regress stor following e and this is the PDF document so it's like tens and tens of pages of regress and Analysis and examples it's it's worth reading but I'm not going to read it in this screencast all right so we want to do a table and we do uh statistics then we do are post estimation table of estim results and then other statistics displayed in E so we need to figure out what those other statistics are I'm going to make this data window a bit smaller so we can see the documentation and um here then uh other statistics we can see that n is the number of obervations sounds useful then we have R square sounds useful r Square adjusted some also useful and then there are other other statistics but these are the ones that you would normally report maybe also F statistic because that's a test statistic and uh sometimes you might have a p statistics for the statistic so that shows the estimat side by side and we can see that our n drops by one because we drop one outlier R square goes up so the model with the Lo transfer dependent variable fits substantially better so that is evidence for for for nonlinearity uh having been an issue and then if we do our resid versus F the plot again a wef plot we can see that it looks pretty good so there's no no evidence of nonlinearity or or heteroscedasticity if you want to um then analyze this data further you can for example turn on the robust standard errors but I don't see any need for it with this data the next thing uh that we need to do is uh to be able to visualize the results but before I go there I'll show you another way of of doing the table so this is like a quick and dirty table that is printed to a console but you might also want to produce a table that you can put in your article so we need to have a table that we can embed in a Word document we can do use St status uh customizable tables and collections framework for that so the collections is kind of like a general framework for constructing tables so you can collect all kinds of Statistics during analysis and then you lay them out in a table then you style the table with a different command and then that produces you very nice PL uh tables that you can then export in various different formats let's take a look at um tables and uh we have customized table of estimation results this is the uh the the better looking table we do launch and then uh M1 M2 and uh the default settings work pretty well so we can just try and one of the problems here is that the dependent variable is different so we need to adjust the settings for this table we do again statistics post estimation and then launch we we recode equations because these are considered different equations because they have different dependent variables so we create so we have old equation name Ln income is going to be income like so so Ln income m income and then we submit and that produces us a nice table so uh as you can see this requires a bit more work and you can customize it this this in many different ways you can for example put a different model or you can put correlation here to the side or you can add whatever statistics so this is a very flexible system if we want to export this we can do a statistics I had to look at the documentations because I did not remember where to collect export command is so we go to uh data and then so statistics summary tables and related uh and then there's summary in Des uh there is uh table of tables and collection build and style table so this is a a table Builder and you can build all kinds of tables here so so we can actually um I'm not going to go through how this works but it's very flexible and we can add add more stuff to the table uh but we have a table here we can just export it and uh we're going to save it as docs and then export it it goes to desktop because that is our working directory so we're going to just call it test table and um okay and then we can click on it and it'll be it will open in word so this is the way that you can get uh tables to Word document and this is how I export every table that I ever do with state if it needs to be in a in a a paper so that is the second way of making uh tables uh for this assignment are doing this quick and dirty table is okay but if you want to be more fancy you can do this table here and then this is exportable to board this one can't be exported just for printing in this data console all right then we need to be able to visualize the results so we have two regressor models and uh let's restore the model one and visualize it so we can do um estimates restore you can also do this from the post estimat menu and then we do Graphics uh statistics post estimation and then um we have marginal effects estimated means interaction so these are basically uh all the very similar commands or these these all run the same command but they they have provid you different options for different use cases and uh I'm more used to this custom and high dimensional analysis this is provides you the most options so I'll just um I'll just run that so uh we want to uh have a factor to compete the margins over for uh we don't need that so that is if we want to C calculate things or plots over different groups so our objective here is to calculate a plot where we have the regression line and uh we can do at so we're going to calculate for example at different levels of income sorry education and uh then we have at specified specification we create and we pick fixed value coari so we pick uh education and that gets from from six to 16 with increments of one year so 16 is about maximum six is about minimum and um then we click okay and that plots us the regression line so what does the line actually look like we click on okay then we can plot it and there is profile plots after margin so we we just run the plot and there are all kinds of options we just do the default so this shows us the regress line and to make this regress line a bit better to show like how well does this regression line explain the data what we can do is is to underly the actual observations here so we can actually show the data underneath this regression line and how you would do it is that you do profile plot and then there is ADD plot we add plot below we create a plot and then the plot is scatter the Y variable is income the X variable is education and then we are we accept and now we have the reron line that explains the data and we can see here that the first model the linear model the line doesn't explain the data well because these data will clearly curve up but the line is straight so that doesn't really work we can visualize the second model which has the log transform dependent variable we will first uh estimates restore the second model so we're going to estimate M2 and now we're going to do statistics uh post estimation and marginal effects estimated means custom and high dimensional Lawns and we're going to specify it as before so this is the same as before yes and now we need to uh specify an expression so uh we can specify a prediction we can create or specify an an expression so um we can do here x predict like so the idea here is that we we exponentiate the predictions because if we log transform the dependent variable then the inverse function of log is the exponential if we don't do that then we get the uh the regression analysis on the original on the log scale so we're just going to do default click okay and then we can do margin spot this is not very useful so because this is now log of salary log of income it doesn't make any sense to take a look at the log of income and um what we need to do instead is to do statistics post estimation and then we're going to predict the exponentiated predictions and then we click okay and then we do our profile plots after marginal analysis and it's it's still flat because the we control for Prestige and this was non significant but we can for example go for for percentage woman and that gives us a more useful plot so we do statistics uh post estimation then uh custom and high dimension analysis let's let's rather have um add so we edit and instead of Education we go from Prestige which is from 20 uh with increments of let's say 10 to 80 so this is the range of the variable that we get from the summary command and we click okay and then we do a margin splot where we change the dependent variable then we need to change also what we plot so we edit the plot and uh instead of plotting income education we plot Prestige and now you can see that this line actually fits the data pretty well so there's still some occupations like this is general managers that are more prestiges that what the model have more income than what the model predicts but you can see here that the are the curve actually fits the data pretty well now when you do these plots you need to pick which variables to plot and I would pick the ones that are statistically significant over those that are not because if there's no no significant results then we can conclude that there is an effect and typically if we can conclude that there's an effect then the estimate the effect is very small and the fly line is pretty flat so I would perhaps go with this Prestige plot and then I would go with our pres woman plot and just show and and then make make a call if it's uh going from the least prestigious occupation that makes about uh 3,000 to the most prestigious ones that are expected to make about close to 15,000 holding education constant and holding share of women constant then uh that's a pretty big effect so interpret you can interpret these extremes or you can directly interet the regression coefficients uh that give you the relative relative effects so um that is uh the mechanics of how you use data to produce uh regression results the various Diagnostics plots two ways of tabulating and then uh how you visualize linear and exponential relationships using the margins the next thing that we need to do is to make uh after do file that we submit as a part of an assignment and also that we convert into a report and how that works is that we open the do file editor and I'm going to put this uh window side by side and now when you start documenting your analysis if you do this kind ad hoc analysis that I just did then the documentation task is is something you do after but in reality how uh researchers tend to work is that you build the do file all the time instead of and you just run it from here and um we start by by taking all the commands here so we're going to copy and paste here so that is our log and if we run this we will get all the results that we got this far that will produce an error so we're going to eliminate everything that we don't need and write some comments and that's what I'm going to do next so I'm going to Lo the data and two slashes is a comment and then um these options you would set them once so there is no need to uh set them again and then we do our univariate you VAR distributions by variat these commands don't change how statea Works they're just there for you to understand what is going on and they're also there for for someone else to understand what your sta code does or what your anal does um documenting your analysis well is super important it is super important for for three reasons and uh one is that you are not documenting it also for for others but also for future you so often time like there's an analysis that you do and then there might be some time that you don't work on it and it might be like you work on it a year later when the paper come back comes back from a a review process and then the reviewers want to see some changes in the analysis then if you have this kind of like completely undoc M analysis it's very difficult to remember what you did and why the second is that if there is more than one person working with the data understanding what the other person is doing is a good idea the third one is the documenting your your code helps you avoid errors so how I actually specify an analysis myself is that I typically write the comments first so I I I plan the analysis in the comments and then I just write the STA commands under the comments so that I I think about the logic of the analysis first and the mechanics later if you think about the logic and the mechanics at the same time but just typing state of commands here then uh it's more error prone than thinking about the logic first by writing the comments documenting what you plan to do and then thinking about the mechanics okay then we have a first regression and Diagnostics then here we would need to have a really good explanation of why we think ministers are outliers because you need to document this kind of decisions but I will just save time not write it here while I'm doing the screencast and um so let's see that's the second regession we store it and then tabulate and then we can do a we will just use the second table and then we can use that table if we want and we're not going to export it then we do Graphics estimat store margin plot we're going to add the the data underneath the plot because that is something that you should do and uh we're going to plot just The Prestige so if we Vis if you visualize the reg models it would makes more sense to visualize the same independent variable in both but this is just to show you how the mechanics work also if you want to do diagnostics then uh a good idea good way to do the Diagnostics is just to copy all this stuff here under regression so you don't need to C uh click on the commands again you can just copy paste the commands here in the doile editor all right so let's say that this is our assignment one this is of course not the full assignment but all these commands that I just demonstrated should be enough for you to complete the assignment and we're going to call it assignment one and then we need to make a report out of it and this is the kind of the hard part in that if you're using an old version of sta or if you have a very exotic uh installation of sta for example if your profile is solely on network drive then this can cause some problems so let's do uh producing the report and we're going to install this package here I have it already installed but I'm going to redo it just that you show it so I'm going to copy paste this and this is a uh something it's a sta package written by this uh this guy called hogish and uh it allows us to make various reports from from sta documents sta doils so what we need to add is to add its installing here in the background and what we need to add here is uh start a log and we're just going to call call it assignment one and then um replace is important because otherwise the uh the log if it's open already if if the log already exists then uh this will cause a failure and another thing that I sometimes do is that I do a capture log close and what this does is that it forces any existing logs to close so if you have a a log open then if you try to open another log it causes an error so before we open a log we need to close an existing log but if you don't have a log open then uh closing a log will causes an cause an error so this capture command here before log close will cause data to ignore any errors that this might cause so what this does is that it uh creates a start a new log or it closes an existing log if it exists and starts a new one and then um we uh log close the log at the end and then finally after each command we need to do this IMG so sorry each figure so um let's see uh these are images and this is just just a kind of like a clunkiness that is a part of the uh the command these are all figures or Graphics this is a graphic and this is a graphic and uh then we do um this is the final lines and now we run this and and it just works it produces a Word document for us before you start adding the log and IMG it's a good idea to check that your data code runs and produces the result that you want it to do but I just did it in one go because uh yeah because yeah there there shouldn't be any errors but there is there is an error because I forgot to change the log name here so it's going to be assignment one instead of report and I'm just going to rerun that line like so and then it gives us a Word document and we can go here and this word document contains a log of everything that we just did and uh then there's all the figures here and how we would start writing a report for the for the assignment the final report we would uh have add some some text here so we would have a style no heading so uh assignment one regression let's call it that then description the assignment and so on and then you can add add line spacing change it to make it look a bit nicer and so on uh then we would for example here when we have the describe we would have let's do here clear formatting explain these results here so you would basically uh just explain what the results are and then you uh interpret everything explain your logic while writing comments in in the word file you submit the word file you submit the do file and then you're done with assign