1. On order to study the relationship between the indices of aggregate final energy demand (Y), real DGP (
), and real energy price (
) for seven OECD countries for the period 1960 to 1982 were collected, and the following model is fitted and the R output is below.
a. Interpret the coefficient estimate of
specific to this problem.
b. Find the change of Y with respect to the rate of change of , at 
and 
, and 
.
c. Is the demand for energy price inelastic? justify your answer. (3 pts.)
d. Test if there is a (first order) autocorrelation in the error term using 
. Make sure to state the null and alternative hypotheses, to provide the values of the test statistic and the critical value(s), and to draw a conclusion. (6 pts.)
2. In order to develop a regression model to predict standby hours of un-unionized graph artists 
, four independent variables, Total Staff present ( ), Remote Hours ( ), Dubner Hours (
), and Total Labor Hours (
), are considered. The following model is fitted and the R output is on page 4.
- Is
rejected? Justify your answer using
.
- Find the estimated regression function. (2 pts.)
c. Find the explained sum of squares (ESS). (2 pts.)
d. Find the degrees of freedom associated with the residual sum of squares (RSS). (2 pts.)
e. Interpret the coefficient associated with the Total Labor Hours ( ) specific to this problem. (4 pts.)
f. Find the standard error of the regression. (4 pts.)
g. Is
? Justify your answer using . (4 pts.)
h. Find the 95% confidence interval for 
.
i. Is there multicollinearity? Justify.
j. Perform the overall significance test for the auxiliary regression of on the remaining X variables using . (Just report the test statistics and the critical value for this test.)
3. In the model considered in Problem 2, we are interested in testing 
using . Refer to the R output on page 5.
a. State the alternative hypothesis (
).
b. Calculate the test statistic for the test.
c. Find the critical value for the test. (4 pts.)
d. Draw your conclusion.
4. Based on a sample of 20 couples, we obtained the following regression model
where 
is the probability of restaurant usage, 
is the income in thousand dollars, and 
is the dummy variable for the need of babysitters such that 
if needed a babysitter and 
if otherwise.
a. Interpret this logit regression model specific to this problem.
b. For a couple with an income of 54 thousand dollars who need a babysitter, find the probability that this couple go to a restaurant.
5. In the study of the relationship between savings (Y) and personal disposable income ( ) and gender, the following model is considered and R output is on pages 7 and 8.
+
,
where 
and 
is the product of and 
.
a. Find the estimated regression line for each gender. (4 pts.)
b. Is the dissimilar model more appropriate than the coincidence model? Justify your answer.
c. In the following regression model, is there strong evidence that the male saves more? Justify your answer.
+
