Department of Economics Ohio Wesleyan University Delaware, OH Economics 251 Research Methods Fall 2015 Daniel Kidane Midterm Exam II This exam is 50 points and will count 15% of your final grade. It consists of two parts and you will have 50 minutes to complete the exam. Part I: Problem Solving Questions Part II: Multiple Choice Questions 1 Question (24 points) 13Questions (26 points excluding the extra credit) The examination is closed book. No books, class notes or any outside materials are permitted during the exam. All scrap paper will be provided in class. For Part I, show all your work clearly to receive a full credit. Please write your answer in the space provided under each question. For Part II, choose the correct letter answer and fill in the corresponding bubble in the provided scantron sheet. Good Luck! Name: ______________________________________ Grading: Part I: _________ Part II:__________ Total (out of 50): ___________ 1 Part I: Problem Solving Question 1. [24 points] Pay equity for men and women has been an ongoing source of conflict for a number of years in North America. Suppose you are interested in investigating the factors that affect salary differences between male and female university professors. You collected a random sample of 100 universities and you believe that the following variables determine a professor's salary: SALARY YEARS EVALUATION ARTICLES GENDER PHD i. Annual Salary Number of years since first degree Mean Score on teaching evaluation Number of articles published A dummy variable; 1 if the professor is male, 0 otherwise A dummy variable: 1 if the person has a PhD, 0 otherwise Using the data stored in Blackboard (Salary), run the initial regression model with all the independent variables and call this model the FULL model. a. [2points] Is the model a good fit? How do you make that decision? b. [2 points] How well does the model explain the dependent variable? c. [5 points] Which independent variable(s) appear to be significant and insignificant at the 10% level of significance? Significance of variables at the 10% level of significance Significant Insignificant 2 ii. Since at least one independent variable appears insignificant, remove the insignificant variable(s) and run a PARTIAL regression. a. [2 points] Write down the PARTIAL regression equation. = b. [5 points] Is it safe to remove the variable(s) in question? Explain how you make that decision. (Hint: a partial-F test could tell you whether it is safe to remove the variable(s) in question. The relevant critical value for this partial F test is 3.942) c. [3 points] Should your FINAL model be the FULL or the PARTIAL model? c. [2 points] According to the FINAL model, interpret the coefficient associated with PhD? d. [3 points] According to the FINAL model, do you observe a statistically significant salary differential between male and female professors? If so, how much is the salary differential? 3 Part II: Multiple Choice Questions [2 points each] 1. In multiple regression analysis, the ratio MSR/MSE yields the: a. t-test statistic for testing each individual regression coefficient. b. F-test statistic for testing the validity of the regression equation. c. coefficient of determination. d. adjusted coefficient of determination. 2. For the following multiple regression model: holding x2 and x3 constant, results in: a. a decrease of 3 units on average in the value of y. b. an increase of 8 units in the value of y. c. an increase of 3 units on average in the value of y. d. None of these choices. a unit increase in x1, 3. A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have a. 121 degrees of freedom b. 135 degrees of freedom c. 130 degrees of freedom d. 4 degrees of freedom 4. What relationship between x and y is suggested by the following scatter diagram? a. b. c. d. a quadratic relationship with downward concavity a linear relationship with negative slope a quadratic relationship with upward concavity a linear relationship with positive slope 4 5. A regression model was fit and the following residual plot was observed. Which of the following assumptions appears violated based on this plot? a. The errors are independent c. No unnecessary outliers b. The variance of the errors is constant d. The errors are normally distributed 6. To explain personal consumption (CONS) measured in dollars, data is collected for INC: CRDTLIM: APR: ADVT: SEX: personal income in dollars the credit limit in dollars available to the individual mean annualized percentage interest rate for borrowing for the individual per person advertising expenditure in dollars by manufacturers in the city where the individual lives gender of the individual; 1 if female, 0 if male A regression analysis was performed with CONS as the dependent variable and CRDTLIM, APR, ADVT, and GENDER as the independent variables. The estimated model was = 2.28 - 0.29 CRDTLIM + 5.77 APR + 2.35 ADVT + 0.39 SEX What is the correct interpretation for the estimated coefficient for GENDER? a. Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be $0.39 higher than females. b. Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be 0.39% higher than females. c. Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be 0.39% higher than males. d. Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be $0.39 higher than males. 5 7. A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y? a. = + + b. = + + c. = + + d. = + + + Use the following information to answer question 8 Suppose you want to improve your GPA, but you are unsure how. You know that you should study more, but there might be some other important factors. So, you sit down and decide that important factors might be the amount of studying, working, partying, and other recreation. You collect data of 100 random students on their GPA, the number of hours of study per week (STUDY), the number of hours they work per week (WORK), the number of times they go to a bar per week (BAR) and the number of movies they rent in the video store per week (MOVIES). You run a regression and get the following output: Regression Statistics Multiple R 0.461 R Square Adj. R Square Standard Error 0.572 Observations 100 ANOVA df Regression Residual Total Intercept STUDY WORK MOVIES BAR 4 95 99 Coeffs 3.421 0.010 -0.010 -0.007 -0.154 SS 8.378 31.090 MS 2.095 0.327 Std. Error 0.203 0.005 0.007 0.026 0.040 F t Stat 16.847 1.931 -1.405 -0.270 -3.895 Sig. F 0.0001 P-value 2.75E-30 0.056 0.163 0.788 0.0002 8. The coefficient of determination adjusted for the degrees of freedom is? a. 0.179 b. 0.212 c. 6.4 d. 3.421 6 9. In multiple regression analysis model selection why do we care more about adjusted R2 than R2? a. because adjusted R2 is always lower than R2 b. because when there is heteroskedasticity R2 will be invalid c. because a new variable we add to the model must significantly contribute to explaining SST before adjusted R2 goes up d. because R2 penalizes the use of irrelevant variables Use the following information to answer the next three questions (#10-12) As part of an effort to induce the public to conserve energy, an economist wanted to analyze the factors that determine home heating costs in the country of Wesleyannia. In Delaware, a capital city of Wesleyannia known for its long, cold winters the economist took a random sample of 35 houses and collected data on the following variables: cost of heating during the month of January (in owucs, the currency of Wesleyannia), house size in hundreds of square feet (Size), number of windows (Windows), and number of occupants per house (Occupants). A multiple regression model for the cost of heating was estimated with the Excel output shown below: Regression Statistics Multiple R R Square 0.554 Adj. R Square 0.511 Standard Error 34.898 Observations 35 ANOVA df SS Regression Residuals Total 3 31 34 Intercept Size Windows Occupants Std Error 4.532 1.489 1.966 6.850 F Sig. F 0.001 37754 84673 Coeffs 11.088 5.632 3.179 15.431 MS 15639.667 t Stat 2.447 3.782 1.617 2.253 P-value 0.020 0.001 0.115 0.032 10. What is the value of the test statistic for the following test H0: 1 = 2 = 3 = 0 against H1: at least one i is different from zero? a. 0.001 b. 12.842 c. 0.554 d. 0.078 7 11. If you wanted to test whether the number of occupants in a home has a positive impact on the cost of heating during the month of January, the resulting p-value would be would be: a. 15.431 b. 0.032 c. 0.064 d. 0.016 12. Ignoring the results from any significance tests conducted on the model, the estimated cost (in owucs) of heating an 800 square-feet house, with 5 windows, and 4 occupants is approximately: a. 35.3 b. 4594.3 c. 4606.6 d. 4578.4 13. How could you fix a problem of serious multicollinearity? a. transform the Y variable b. transform both the Y and X variables c. add a time related variable to the model d. try to identify and exclude one of the independent variable that is duplicative Extra credit: You can earn 2 points if you answer the question correctly and if attendance guidelines have been met. 14. All of the following are important values one should consider when doing model assessment and model selection, EXCEPT: a. SST b. F-test for overall validity of the model c. adjusted R2 d. t-test for each individual slope estimate 8 Gini 0.35 0.46 0.36 0.48 0.52 0.5 0.61 0.5 0.49 0.45 0.54 0.66 0.57 0.5 0.43 0.49 0.56 0.52 0.58 0.61 0.54 0.61 0.42 0.42 0.33 0.52 0.37 0.38 0.3 0.43 0.32 0.37 0.31 0.35 0.32 0.31 0.39 0.24 0.25 0.18 GNP GDP growth URBAN LITERATE EDUCATION POPULATION AGRICULTURE SOCIALIST 63 2.5 7 10 0 1.7 55 0 84 3.6 18 24 23 2.3 50 0 73 2.7 6 5 0 2.7 66 0 70 5.4 5 17 2 3 57 0 93 0.3 12 20 4 2.6 37 0 92 8.2 13 58 8 3.1 40 0 224 5.1 23 47 8 2.7 37 0 150 5.1 30 72 26 3 26 0 150 4 18 41 1 2.9 11 0 248 5.9 38 51 11 3.5 32 0 251 5.1 47 61 12 2.9 34 0 202 5.9 34 67 12 3.3 33 0 297 5.4 47 61 18 2.9 26 1 156 4.6 32 40 12 2.1 24 0 423 6.5 34 84 21 3.5 29 0 427 4.2 69 84 24 2.1 11 0 388 4.5 30 82 43 1.7 10 0 454 4.9 35 60 19 2.5 12 0 464 7.3 50 62 11 3.4 16 0 231 8 45 61 11 2.9 16 0 560 7.8 41 78 29 3.1 23 0 172 6.1 43 15 19 3.2 17 0 460 1.2 73 90 37 0.6 19 0 681 4.2 71 91 31 1.4 17 0 451 6.8 28 77 34 1 24 1 750 5.9 68 65 21 3.4 6 0 341 6.9 43 80 41 0.6 23 0 572 7.3 57 87 23 1.1 21 0 686 8.5 78 84 48 3.3 11 0 91 2.9 9 9 3 2.2 58 0 1599 2.9 78 98 67 0.6 4 0 1800 3.9 76 99 73 1.7 14 0 780 10.5 63 98 74 1 15 0 1609 4.9 37 99 56 0.8 9 0 2057 5.6 69 98 50 1.8 6 0 3603 4.3 70 98 64 1.2 4 0 2220 4.4 72 99 55 0.7 7 0 870 3.8 40 97 47 0.3 24 1 649 4.3 47 98 50 1 26 1 880 3.2 47 95 25 0.5 16 1 ( SSR f SSRr ) Fk d ,( n k 1) f kd MSE f To find the critical F value use FINV function Or, you can compute the P-value using FDIST and comapre it with alpha