Lab 3: Regression

Due by 2:20 PM on Wednesday, October 6, 2021

Lab Content

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Materials

Objectives

By the end of this tutorial you should be able to complete the following tasks in Stata:

  • Estimate and interpret a simple (two-variable) linear regression in levels, using continuous and binary variables, and use heteroskedasticity-robust standard errors.

  • Identify \(\hat{\beta_0}\), \(\hat{\beta_1}\), standard errors, \(SST\), \(SSE\), \(SSR\), and \(R^2\) in Stata output and interpret them

  • Calculate predicted values and residuals

  • Create scatter plots

  • Estimate a multivariate linear regression

Key commands

commanddescription
Estimation commands
regress var1 var2Estimate a regression, with var1 as the dependent variable and var2 as the independent variable(s)
regress var1 var2, robustEstimate a regression with heteroskedasticity-robust standard errors
correlate var1 var2 ... varnCalculate correlation coefficients of all listed variables, from var1 to varn.
graph twoway scatter var1 var2make a scatter plot with var1 on the y-axis and var2 on the x-axis.
Post-estimation commands1
predict newvar, xbUse estimated regression coefficients to predict \(\widehat{y}\). It will generate newvar2
predict newvar, residualsUse estimated regression coefficients to predict residuals, generating newvar3
Working with data, missing values
count if var1 == 1count observations if the expression var1 == 1 is true
count if !missing(var1)count observations if var1 is not missing
drop if missing(var1)drop all observations where var1 is missing
tab var1, missingInclude missing values in tabulation

Reading regression tables

labelled Stata output

Lab 3 Exercise

What do I submit?

  • Your written up answers to exercise questions (1) - (13). This can be typed or written out then scanned (or photographed), in any reasonable format.
  • The do-file you’ve created that runs this analysis
  • A log file that contains the results from this exercise.

Questions

Today, we’re going to look around at the graduation data set that we discussed in class, graduation.dta.

  1. Download the do-file template and data files. Personalize the file paths so that you can run it and open your graduation.dta file. You can also work with a blank data file if you’re more comfortable - just make sure you remember to include commands to start and close your log file.

  2. Take a look at graduation.dta. How many observations are there? What is the distribution of treatment arms?4

  3. There are six continuous food security variables5. You can look for them with lookfor fs. Pick one variable and write out a population model to determine the relationship assignment to graduation and food security. For the rest of this lab, I refer to the variable you chose as foodsecurity. If that’s going to irritate you, you can rename your variable like this: rename fsec5 foodsecurity, using the variable name that you’ve chosen in place of fsec5.

  4. Tabulate your food security value and check for missing observations. Drop any observations for which you have missing values of foodsecurity (see above for how to do this). How many observations are remaining?

  5. Make a scatter plot of the relationship between your chosen food security variable and graduation (Include this in your submitted problem set). Is this easy to interpret? Calculate and report the associated correlation coefficient.

  6. Conduct a t-test of whether the mean of foodsecurity is different between those who did and did not receive the graduation program6

  7. Estimate the relationship between your chosen food security variable, foodsecurity and assignment to graduation, graduation using simple linear regression, with standard (homoskedasticity-assumed) standard errors. How do your t-statistics compare to what you found in the previous t-test? What was the impact of assignment to the graduation program on food security, based on your regression?

  8. Re-estimate your regression, and this time adjust your standard errors to be heteroskedasticity-robust. Fill in the chart below with your estimates.

VariableEstimateVariableEstimate
\(\hat{\beta_0}\)\(\hat{\beta_1}\)
\(R^2\)\(TSS\)
\(ESS\)\(SSR\)
d.f.\(SER\)

  1. After that regression estimate, generate a new variable, predict_fs equal to the predicted value of your food security variable. Generate a second variable, resid_fs equal to the residual.

  2. What is the mean of each variable? How does the mean of predict_fs compare to mean of foodsecurity in your sample?7

  3. Examine the predicted value of your food security variable, predict_fs, for the youngest person in your sample.8 What is its residual?

  4. When we estimate a linear regression with no coefficients, sometimes we’ll say we are “regressing on a constant.” Regress foodsecurity only on a constant. What is \(\hat{\beta_0}\), and how does it compare to overall mean?

  5. For this final step, I’d like you to play around with the data. Pick one continuous dependent variable and one continuous or binary independent variable.9 You can look at the correlation between two variables, or you can look at the impact of one of the program dimensions (group coaching, group livelihood, etc) on an continuous outcome of interest.

    1. Write a population model you want to estimate.
    2. Estimate it using OLS, adjusting your standard errors to be heteroskedasticity robust. Write an equation that reflects your estimated model in the form \(\hat{y}=\hat{\beta_0} + \hat{\beta_1}x\), replacing \(y\) and \(x\) with your chosen varables and replacing \(\hat{\beta_0}\) and \(\hat{\beta_1}\) with your estimates.
    3. In 1-2 sentences, , what do your results tell you, collectively?

Video Recording

  1. Post-estimation commands must be run immedately after a regression, while the regression results are still held in your local variables↩︎

  2. Here, newvar equals \(\widehat{newvar_i} = \widehat{y_i} = \widehat{\beta_0} + \widehat{\beta_1}x_i\)↩︎

  3. Here, newvar equals \(\widehat{newvar_i} = u_i = y_i - \widehat{\beta_0} + \widehat{\beta_1}x_i\)↩︎

  4. There are a few variables here, including treatment_arm↩︎

  5. Not fsec7, which is categorical, or fsec which is always equal to 1↩︎

  6. Hint; ttest var1,by(var2) will run a t-test of the mean of var1 are equal for two groups determined by var2. ↩︎

  7. If they differ, you should make sure you have dropped all missing values of foodsecurity! Try sum predict_fs foodsecurity to see if the sample sizes are the same↩︎

  8. Now is a good time to try out lookfor age↩︎

  9. Categorical variables that take on a just few observations, like the identity of your head of household, won’t work here. You’ll need to tabulate the variables to see what you’re working with↩︎

Last updated on October 5, 2021

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