ECON 306 Homework 3 complete solutions correct answers key

ECON 306 Homework 3 complete solutions correct answers key

Instructions: Please print out and complete the following assignment writing your answers clearly and showing your work directly on the assignment. Please keep a log of your work in STATA and print out and attach all of your results. Use a highlighter to highlight all of your commands in STATA (this will make it easier for the graders to see your work). Follow directions carefully (underlining or circling where indicated in your STATA output). Be sure to turn the assignment in at the beginning of class on Tuesday, March 1. Late homeworks cannot be accepted.

 (30 points total.  10 parts worth 3 points each.)

With this assignment you will find an Excel file called hw3.sleep.xlsx. For reference, the variables in this file are:

sleep = minutes of sleep at night per week

totwrk  =  min worked per week

educ = years of schooling

age =  in years

earnings =  total earnings for the year

a.       Run the following regression: (Label this Model 1)

b.      At a level of α=.05, for which, if any, values of βi, would you reject the null hypothesis that βi=0? (If this applies, write your answer in the space below AND circle in the STATA output)

c.       What percentage of the variation in sleep is explained by the X-variables? (Write your answer below and underline in STATA output)

d.      What is the predicted  sleep with totwrk=2400, educ=16, age=28, earnings=41,000? 

e.       According to this model, how much will sleep change as totwrk increases by 300 minutes per week?

f.       Test the hypothesis that the coefficients on educ and age are jointly significant at a level of α=.05. Do this by (1) writing down the formula for the relevant F-statistic in the space below using the formula from class. Calculate it by running the appropriate restricted regression (this restricted version of the regression will be called Model 2.)  (2) Indicate the critical F-value below and make a decision about the hypothesis.

g.      After calculating the F-statistic this way, run the appropriate STATA command to confirm your answer (the “short-cut” way discussed in class). Circle this in the STATA output.

h.      Return to Model 1.  Now test the hypothesis that all 4 of the variables have a coefficient of zero (test of overall significance) at a level of α=.05. Do this by (1) writing down the formula for the relevant F-statistic in the space below using the formula from class. (2) Indicate the critical F-value and make a decision about the hypothesis.

i.        Confirm your results by indicating that the STATA output shows the same answer (circle in the STATA output).

Run a regression of sleep on the variable age only.

j.        What can be said about the relationship between the t-statistic for the age coefficient and the F-statistic in this scenario? Explain why this is.