In this question, you will apply the FWL theorem to estimate a regression coefficient using the birth—weight smoking dataset

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Before von start, itiake sure you have installed and loaded these packages: haven, ggplot2, dplyr. tidyverse,stargazer, AER, MASS. and car

Question 1: Frisch- Waugh-Lovell Theorem

In this question, you will apply the FWL theorem to estimate a regression coefficient using the birth—weight smoking dataset

Regress the variable birt.liweight’ on tue the varial)lcs sinoker. unmarried’. and ‘nprevisC.

Save the residuals as resids 1

Regress the variable drinks’ on the variables ‘smoker’, umnarried’, and nprevist’. Save the

residuals as resids2

use your results from (a) and (b) to estimate the coefficient on ‘drinks’ in the regression of birthweight on drinks’, smoker’, ‘unmarried’, and ‘I11)revist Note: You must use the results from (a) and (b), and time Frischi-Waugh theorem to answer this part of the question. Compare the coefficient you obtained using the Friscim—Waugh theorem to that when estimating the time full model using the 1mo function.Regress ‘birthweight’ on drinks’, ‘smoker’, ‘unmarried’, and ‘nprevist Report the results of the regression in a table (using the stargazer() function

Question 2: Dummy Variables, Interaction Terms

In this question you will ijeed to use the CollegeDistance dataset contained in the AER package. You must

install and load time AER package to access the dataset.

# After installing and loadzng the AER package, you can access the data using this command:

data (“CollegeDistance”)

Create a dummy variable called ‘hispanic’ that is equal to 1 if ‘ethnicity’ = “hispanic”,

and () otherwise. Create a dummy variable called ‘afam’ that is equal to 1 if ‘ethnicity’ = “afam”,

and (J otherwise. Create a duinniy variable called ‘male’ that is equal to 1 if ‘gender’ = ‘iiiale”, and O otherwise.

lise the dummy variables you created iii (a) to run a regression of ‘cðucation on score’,

‘afarmi’, ‘hispanic’, ‘male’, and ‘distance’. Report time results of this regression in a table using time stargazer() function.

Suppose you believe the effect of score on educational attainment differs based on gender.

Adjust the regression in part (b) to include an interaction terni l)etweeII ‘timale’ and ‘score Report the results of this new regression in a table using the stargazer() function.

Question 3: Joint Hypothesis Testing and R2

In this question you will need to use the MASchools dataset contained in the AER package. You nmust install and load the AER package to access the (lataset.

# After znstall’ng and loading the AER package, you can access the data using this command:

data (“MASchools”)

Create a new data frame called ‘MASchools_subset’ containing only the ‘expreg’, ‘strat.io’, ‘in conic’, ‘scoreS’, and ‘english’ columims. Drop any observations with an NA value from ‘MASchools_subset You can access time help file for the MASchools (lataset using time ?MASchools conunan(1 Regress ‘scoreS’ on ‘expreg’, ‘stratio’, ‘inconic’, and ‘english’ using observations from  1\lASchools subset.

Calculate the SST (Total Stun of Squares) of the regression estimated in (b), where SST = — V)2 save the result. Calculate t.he SSR (Residual Sum of Squares) of the regression estimatedin (b), where SSR = (ij )2. Save the result. Hint.: use the residuals() function

Attachments:

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