Only need help with question 2. Please provide only the code for R needed to solve the questions instead of answering question 2.

ECO 321 Fall 2020 Homework 3 Due October 9 by 5 pm Cut and paste at the end of your submission the R code you have used to Show your work. 1. Let us consider the following regression model for a sample of in female workers WorkHoursi = [30 + IChildi + m, i: 17 . . . ,n, (1) where Childz- is a binary variable that takes value 1 if the individual has one or more child and 0 otherwise; and WorkHours is the individual's usual hours worked per week in past 12 months. Let WeeklyPay = Y and Child = X. Also let n1 the number of individuals who has a one or more than one child and no the number of female worker who does not have a child, such that no + m = n. Recall that the OLS estimators are given by Exam-Ye-X) a=rax (a) Let \"9230 an individual 773 working hours for which the value of X is 0; and gig; an individual i's working hour for which the value of X is 1. Show that n ng m ElieY) (xiX):%Zyi,1_% yin i:1 1':1 i:1 (b) Show that i (II) _ X)2 : \"In- 1'21 n (c) Use the results in (a) and (b) to conclude that 1 = )71 176: upon an appropriate denition of 171 and 170. (d) Show that 17 =(n1)171 + (no)l70. (e) Using the result in ((1), nally Show that Bo = 170. 2. The data file, female_work.csv, is a subset of The American Community Sur- vey(ACS) for the year 2018, with only female workers from age 18-40. A detailed de- scription of the variables contained in the file is given in the pdf file Documentation.pdf available on Blackboard. You can find a sample code for fitting and testing a linear regression model in R inside the folders called "Chapter 2: Linear Regression with One Regressor" and "Chapter 3: Inference in the Linear Model with One Regressor" on Blackboard. (a) Suppose that all assumptions for OLS are satisfied and estimate the simple regression model in equation (1) using heteroskedasticity robust standard errors. (b) Report the values for Bo and B1. (c) What does the sample statistic Bo capture? (d) Do women with child work less? By how much? Explain. (e) Is the estimated effect of having child on women's working hours statistically significant? Carry out a test at the 1% level. (f) Construct a 95% confidence interval for the effect of having children on working hours