3E03_Final_20191__1_.pdf

Student Name: Student Number: 6. The interpretation of the slope coe ffi cient in the model Y i = β 0 + β 1 log( X i ) + u i is as follows: (a) a change in X by one unit is associated with a β 1 · 100% change in Y . (b) a change in X by one unit is associated with a β 1 change in Y . (c) a 1% change in X is associated with a β 1 % change in Y . (d) a 1% change in X is associated with a change in Y of 0 . 01 · β 1 . 7. In a prediction problem, there are: (a) specific regressors of interest. (b) control variables. (c) predictors and the variable to be predicted. (d) never situations where OLS overfits data as long as there are a large number of regressors relative to the number of observations. 8. Consider the following regression model: TestScore = β 0 + β 1 inc + β 2 inc 2 + u where inc denotes income. You have variables, testscore , inc , and incsq in the data set. Write the R command to run estimate the above nonlinear regression function. If you have been using a software di ↵ erent from R, write the name of the software (e.g. STATA, Matlab, Python) and write the relevant commands of the software. 9. Consider the following regression model: log( Wage ) = β 0 + β 1 Educ + u where Educ is years of education. We can think individual ability as an omitted variable. When we omit ability, will the estimated value of β 1 be higher (overestimated) or lower (underestimated) than the true e ↵ ect of education on wage? 10. Suppose that you have 1,000 candidate predictors. If you believe that only few predictors are relevant, which methods will you choose between ridge and lasso? Page 3 of 10 ch8 - - v ⑳ - overestimated

Student Name: Student Number: Part C. (30) In the following model, we study the tradeo ↵ between time spent sleeping and working and to look at other factors a ↵ ecting sleep: sleep = β 0 + β 1 totwrk + β 2 educ + β 3 age + u where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. 1. (5) Jake thinks that educ and age do not have any e ↵ ect on sleeping time. Write the null hypothesis to test his idea. 2. (5) What is the R command to test the above hypothesis? Complete the necessary package name and the final command for the F-test. If you have been using a software di ↵ erent from R, write the name of the software (e.g. STATA, Matlab, Python) and write the relevant commands of the software. library(lmtest) library(sandwich) library( ) sleep.m = lm(sleep ~totwrt + educ + age) (Command for F-test here) Page 6 of 10 - Ho: =0 and : 0 Ha: either B20 or B30 or both

Student Name: Student Number: Part D. (20) A researcher is interested in predicting average test scores for elementary schools in Arizona. She collects data on three variables from 200 schools: average test scores ( TestScore ) on a standardized test, the fraction of students who qualify for reduced-priced meals ( RPM ), and the average years of teaching experience for the school’s teachers ( TExp ). The table below shows the sample means and standard deviations from her sample. Variable Sample Mean Sample Standard Deviation TestSchore 750.1 65.9 RPM 0.60 0.28 TExp 13.2 3.8 After standardizing RPM and TExp and subtracting the sample mean from TestScore , she estimates the following regression: \ TestScore = - 48 . 7 · RPM + 8 . 7 · TExp, SER = 44 . 0 1. (5) You want to predict average test scores for an out-of-sample school with RPM = 0 . 52 and TExp = 11 . 1. Compute the standardized values of RPM and TExp for this school. Recall that a random variable X ⇤ is standardized as mean 0 and variance 1 if we compute X = ( X ⇤ - E ( X )) /sd ( X ). 2. (5) Compute the predicted value of average test scores for the school in Question 1 . (Hint: The model subtracts the sample mean of TestScore ). Page 9 of 10 did'nt do !