[45 Minutes.] Discovered by psychologist Angela Duckworth, "grit" is a personality trait that reflects passion and perseverance for long-term goals. Individuals with higher grit scores tend to be more likely to accomplish long-term goals. Below is a table of regression output produced in Stata using data on university students. The data contain (i) students' average first-year university grades (Uni Grade), measured from 0 to 100; (ii) their grit scores (Grit Score), measured from 1 to 5; and (iii) their incoming high school grade average (HS Grade), measured from 0 to 100. The first regression, reported in column (1), is a simple regression of the university grade on the grit score. The second column is a simple regression of the university grade on the high school grade. The third column is a multiple regression of the university grade on the grit score and high school grade. The fourth column is a multiple regression of the natural log of the university grade on the grit score and the natural log of the high school grade. The numbers listed in the table are the estimated coefficients from each regression, with standard errors listed under the estimate in parentheses. 12 is the R from each regression and "rmse' is the root mean square error from each regression (i.e., o from our lecture slides).Regression Results Grit Score H5 Grade 1n(H5 Grade) Constant Observations r2 rmse {1) Uni Grade 9.3495 (9.5229) 94.9139 (1.9292) 133? 3.3313 13.1313 Standard errors in parentheses (2) Uni Grade 9.4912 (9.9349) 29.4433 (2.3923) 133? 3.3313 15.4433 (3) (4) Uni Grade 1n(UniGrade) 3.5115 3.3312 (9.5939) (9.9992) 3.4333 (9.9343) 1.2333 (3.3261) 25.9325 -1.54G? (3.2991) (9.3352) 133? 133? 3.3315 3.1233 15.4435 3.2352 Please write your answers to all questions below on paper (or in another file), take pictures of or scan the pages with your answers, and then upload all the files with your answers below. Clearly indicate where we can find your answer to each part in the files you upload. Part A. Interpret the estimated coefficient on Grit Score in column (1). Be precise in your answer, explaining what the number means. (5 marks) Part B. Explain why the coefficient on Grit Score changes the way it does between columns (1) and (3). Be precise. (8 marks) Part C. Interpret the coefficient on Grit Score in column (4). Be precise. (5 marks) Part D. Suppose you run a new regression with Grit Score as the dependent variable on the High School Grade as the independent variable. What is the value of OLS slope coefficient from this regression? (7 marks)