as many questions in the packet as possible
Exam 1. Econ 253. fall 2022 Dr. Averett 1 | P a g e Name (first and last):_________________________________________ Directions: Please answer each question after reading it carefully. If anything is unclear, please write out any assumptions you make to answer the question. Please do not leave blanks as I do offer partial credit. Good luck. Budget your time carefully-go through and answer all that you know well and then come back to any that you need more time for. Part 1. True/False questions. You must provide an explanation even if the answer is true. No guessing for credit. No explanation, no credit. 3 points each. 1. If SSR= 2* SSM where SSM is Model Sum of Squares 2 1 ˆ( ( ) ) n i i y y = −∑ and SSR is the Sum of Squared Residuals 2 1 ˆ( ) n i i ε = ∑ , then the R2 = .50. Justify your answer with an explanation 2. In a bivariate regression, if I want my sampling distribution for 1̂β to be wide, I want considerable variation in my X variable. Exam 1. Econ 253. fall 2022 Dr. Averett 2 | P a g e 3. Reducing the significance level, α, will increase the probability of making a Type I error. 4. Suppose that true core model has two X variables. In this case an omitted variable (X2) that is uncorrelated with X1 will not result in omitted variable bias. 5. Suppose that true core model has two X variables. If the true ??1 is positive and the estimated 1̂β is negative, then it must be the case that the correlation of the omitted variable and X1 is negative. 6. One advantage of a randomized controlled experiment is that the results are always externally valid. 7. A null hypothesis and an alternative hypothesis are statements pertaining to sample statistics. Exam 1. Econ 253. fall 2022 Dr. Averett 3 | P a g e Part II. Longer answer. Show all work. Point values in parentheses 1. Suppose we are interested in knowing the relationship between hours studied and scores on a Spanish exam. a. Suppose some kids don’t study at all but ace the exam, leading to a bivariate OLS result that studying has little to no effect on the score. Would you be convinced by these results? Explain. (2 points) b. Write down a model and explain your answer to (a) in terms of the error term. (3 points) c. What if some kids speak Spanish at home? Discuss implications for a bivariate model that does not include this factor and a multivariate model that controls for this factor. Be specific. Is there omitted variable bias? What direction is the bias? What assumptions are you making? (4 points) Exam 1. Econ 253. fall 2022 Dr. Averett 4 | P a g e 2. The next set of questions are based on the following regression where Y=your college cumulative GPA, alcohol=average avg # days per week drink alcohol, skipped=average number of lectures skipped per week. ------------------------------------------------------------------------------ . regress colGPA alcohol skipped Source | SS df MS Number of obs = 141 -------------+---------------------------------- F(2, 138) = 6.09 Model | 1.57451595 2 .787257973 Prob > F = 0.0029 Residual | 138 .129214373 R-squared = 0.0811 -------------+---------------------------------- Adj R-squared = 0.0678 Total | 19.4060994 140 .138614996 Root MSE = .35946 ------------------------------------------------------------------------------ colGPA | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- alcohol | .0322789 .0234786 1.37 0.171 -.0141454 .0787031 skipped | -.1032821 .0296414 -3.48 0.001 -.1618922 -.044672 _cons | 3.10653 .0544492 57.05 0.000 2.998867 3.214192 ------------------------------------------------------------------------------ . sum colGPA hsGPA alcohol skipped Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- colGPA | 141 3.056738 .3723103 2.2 4 alcohol | 141 1.901064 1.374701 0 7 skipped | 141 1.076241 1.088882 0 5 a. Interpret the coefficient on skipped. Do not use the words unit in your answer. (3 points) b. Explain why having a small SE ( 1̂β ) is so important in your model (3 points) Exam 1. Econ 253. fall 2022 Dr. Averett 5 | P a g e c. Is the variable alcohol statistically different from zero? Show all your work. Use an α of .01. You may use the p- value method or the t-statistic method. If you use the latter, use a tcritical of 2.40. (3 points) d. What is the unit of observation? (2 points) e. It looks like Stata did not report the residual sum of squares. Calculate this number. (3 points) f. Calculate the sum of the residuals. (3 points) Exam 1. Econ 253. fall 2022 Dr. Averett 6 | P a g e g. Calculate the predicted colGPA for a student who skipped an average of 1 class per week but does not drink alcohol. (3 points) h. Calculate the residual for a student with a 4.0 who skipped an average of 1 class per week but does not drink alcohol. (3 points) Exam 1. Econ 253. fall 2022 Dr. Averett 7 | P a g e 3. Suppose you have a sample of 10 individuals, and you have collected data on their number of children (X) and their annual hours of lost sleep (Y). You know that 1 ( )( ) n i i i x x y y = − −∑ = 1,070 and that 2 1 ( ) n i i x x = −∑ =14.1. Furthermore, you know that the mean of lost sleep ( )Y is 190 and that 1 17 n i i x = =∑ You also know that 1 17 n i i n x = × =∑ . Using this information, calculate the slope and intercept estimates using the OLS method for the following model: 0 1i i iY Xβ β ε= + + . Show all your work to receive full credit. At the end, write your fitted equation and circle it. (8 points) Exam 1. Econ 253. fall 2022 Dr. Averett 8 | P a g e 4. You have been hired by our local hospital, IMSICK, to investigate what factors lead to more doctor visits. You have cross sectional data where the unit of observation is a patient. You regress numvisit (number of doctor visits in the past year) on the patient’s age. . regress numvisit age Source | SS df MS Number of obs = 2,227 -------------+---------------------------------- F(1, 2225) = 26.00 Model | 414.714186 1 414.714186 Prob > F = 0.0000 Residual | 35490.3428 2,225 15.9507159 R-squared = 0.0116 -------------+---------------------------------- Adj R-squared = 0.0111 Total | 35905.057 2,226 16.1298549 Root MSE = 3.9938 ------------------------------------------------------------------------------ numvisit | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------------------