Question 1
18 pts
Use the following information:
99% Confid
Variable Observation betal SE(betal) nee
Interval
Term GPA XXXXXXXXXX XXXXXXXXXX, XXXXXXXXXX]
Round to 2 decimal places where necessary. Leave answers as decimals, not percentages.
A. How many degrees of freedom do we have?
B. What is our significance level, a?
C. Using the above significance level, in the T-distribution, what is the area under each tail?
D. Calculate the t,,_1 7 critical value.
ound until the very last step.
Round to 2 decimal places. Hint: Don't
Question 2 18 pts
You collect a sample of data surveying Americans on their marital fidelity. That is, you are interested
in collecting data on the characteristics associated with cheating and non-cheating spouses. Assume
there is no selection bias (or response bias, really) and that the sample was randomly drawn. You
hypothesize that there is a relationship between someone's age and the number of affairs they
engage in. You estimate the following regression:
Af fairs; = Bo + Br Age: + ui
Stata gives you the following results:
Source SS df Ms Number of obs = 601
—— F(1, XXXXXXXXXX
Model XXXXXXXXXX219586 Prob > F = 0.0195
Residual XXXXXXXXXX XXXXXXXXXXR-squared =
Total XXXXXXXXXX8818026
naffairs Coef. Std. E
.
age XXXXXXXXXX
_cons XXXXXXXXXX
Answer the following. Round to 2 decimal places.
A. First, we want to test whether or not the variable AGE is statistically significant at the 10% level.
That is, test whether or not the coefficient for Age is statistically different from 0. Calculate the T-
stat associated with the point estimate for the variable AGE.
B. Calculate the critical value for the 10% significance level, given the information in the image
above. Use the Z-distribution. Keep the value as positive.
C. Can we reject the null that Age has no statistically significant effect on the number of affairs at
the 10% significance level? That is, is there a statistically significant effect of Age as a predictor of
the number of affairs? Answer "Reject" or "Fail to Reject"
D. Calculate the R? value. The print out gives you the "SS residual” and "SS Total" values. Round to 2
decimal places. Do not put your answer in percentage form.
E. TRUE OR FALSE: Given your above value for the R?, this model explains the variation in the
number of affairs people have pretty well. That is, this model, using age as the explanatory variable,
has good predictive power for the number of affairs people have. Answer "TRUE" or FALSE".
Question 4 24 pts
Wage regression
Suppose the following table is a random sample of five workers from the pool of employees in Santa
Cruz There are two variables "wage" and "educ,” which measure hourly wages and years of
education, respectively.
id wage educ
1 13 12
2 15 16
3 10 9
4 30 18
5 14 16
Suppose we have the following population regression model to investigate how an extra year of
education affects wages:
wage = fy + Breduc + u, Eluleduc] = 0
where u is an e
or term.
Following the next steps, estimate the slope and intercept parameters by OLS. Note that you DO
NOT need to use Stata for this question. All calculations should be done by hand or calculator.
A. Compute the sample average of hourly wages. (Round your answer to 1
decimal place)
B. Compute the sample average of years of education. (Round your answer to 1
decimal place)
C. Compute the sample variance of years of education. (Round your answer to 1
decimal place)
D. Compute the sample covariance between hourly wages and years of education.
(Round your answer to 1 decimal place)
E. Using your answers in parts C and D, compute an OLS estimate for the slope parameter.
(Round your answer to 2 decimal places)
F. Using your answers in parts A, B, and E, compute an OLS estimate for the intercept parameter.
(Round your answer to 2 decimal places)
Question 5 8 pts
Suppose we have the following simple linear regression (SLR) model:
y =F +hiz+u Blulz] =
To estimate the intercept and slope parameters in this population model, you are given the following
sample statistics computed from a random sample of {z:, y; }:
+ (sample) covariance between x and is 10.
+ (sample) standard deviation of x is .5.
+ (sample) standard deviation of y is .2.
A. Using these statistics, compute an OLS estimate for the slope parameter.
(Hint: The answer is an integer.)
B. Suppose you are given the following extra sample statistics:
+ (sample) average of x is 2.
+ (sample) average of y is 100.
Using the extra statistics and your answer in part A, compute an OLS estimate for the intercept
parameter. (Hint: The answer is an integer.)
Question 3 45 pts.
Hollywood Accounting
For this question, download the following data: PS2MoviesA.dta L . You will need to use Stata to
answer the following questions. Round your answer to 2 decimal places. unless stated otherwise. If
the answer is negative. include a negative sign.
You are an analyst working at the independent film studio, A24, who has been assigned
to analyze the economics of Hollywood movies.
A. In our sample, what is the average budget of movies? Scale your answer by $100,000. You can
either create a scaled variable or just divide your answer by 100,000. Your answer should be in
terms of 100,000.
B. Which movie had the biggest budget? Write the co
ect number next to the co
ect mo
example, if you believe the answer is option 34, type in "34." in the box (without quotes)
1. Captain America: Civil Wa
2. Batman v Superman: Dawn of Justice
3. The Ho
it: Battle of the Five Armies
4. Ha
y Potter and the Half-Blood Prince
5. Pirates of the Cari
ean: On Stranger Tides
6. No Time To Die
7. Shrek the Third
C. What is the median revenue of a movie with an average score of 6 or less? The variable
Vote_average measures a movie's average rating. Do NOT scale your answer.
Create a new random variable, profit, that shows a specific movie's profit. Remember, Profit =
evenue - budget. Because these are large numbers, let's scale this profit variable by 100,000.
D. How many movies had a positive profit? That is, made money?
E. How many movies lost money?
F. How many movies
oke even? That is their revenue matched their budget?
G. You believe that there is some relationship between a movie's profit and its average rating.
Calculate the covariance between these two variables. Round to 2 decimal places if necessary.
H. Similarly, calculate the co
elation between these two variables in part G. Round to 2 decimal
places if necessary.
1. More specifically, you believe it takes on the following relationship:
Profits = fy + 1 AvgRating + u
First, what Is Bp? Round to 2 decimal places if necessary. Include a negative sign if necessary.