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Question 1 18 pts Use the following information: 99% Confid Variable Observation betal SE(betal) nee Interval Term GPA 680 2.601 0.0282468 (2.545538, 2.656462] 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. round 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, 599) - 5.48 Model 59.219586 1 59.219586 Prob > F = 0.0195 Residual 6469.86194 599 10.8011051 R-squared = Total 6529.08153 600 10.8818026 naffairs Coef. Std. Err. age .033822 .0144444 _cons .357114 .4880375 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 error 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 correct number next to the correct mo example, if you believe the answer is option 34, type in "34." in the box (without quotes) 1. Captain America: Civil War 2. Batman v Superman: Dawn of Justice 3. The Hobbit: Battle of the Five Armies 4. Harry Potter and the Half-Blood Prince 5. Pirates of the Caribbean: 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 = revenue - 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 broke 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 correlation 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.