1. With this assignment you will find a data file called HW3.Sleep. This data represents a part of a study that looked at the tradeoff between time spent sleeping and working as well as other factors that affect sleep. For reference, the variables in this file are:

sleep = min sleep at night, per week

totwrk = min worked per week

educ = years of schooling

age = in years

Open this dataset within STATA. Before you begin answering the following, it's not a bad idea to ask STATA to summarize the data using the commands summarize. As you complete this assignment, be sure to save/store all of your STATA results.

a. Run the following regression: (Label this Model 1 in your STATA output)

(Sleep)^{^} = β₀ + β₁ * totwrk + β₂ * educ + β₃ * age

b. At a level of α = .05, for which, if any, values of βi, would you reject the null hypothesis that β_i = 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 three X-variables? (Write your answer below and underline in STATA output)

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

e. According to this model, how much will sleep change as age increases by 15 years?

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 perform a 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).

2. Suppose you are running a model to look at the determinants of earnings. After running your data in STATA, you get the following output:

Several of the numbers in the STATA output have been intentionally covered up.

a) Solve for the standard error of the coefficient for height (Show your work):

b) Solve for the t-statistic for education (Show your work):

c) Solve for the coefficient for age (Show your work):

d) Interpret the F-statistic and corresponding p-value STATA has calculated. What does this tell us?

Consider a model where we regress Earnings on Height only:

d) What is the value of the t-statistic for height? Explain how you know this.

Attachment:- Assignment.rar