5) Below is a regression model that estimates the relationship between test scor

Question

5) Below is a regression model that estimates the relationship between test scores and hours studying mathematics. Where College GPA for student i is a function of their entering ACT score (ACT), the average number of lectures they miss per week (SKIPPED), an indicator for whether or not they are male (MALE), and a random error term . Note, the mean of College GPA is 3.06 ( = 0.37). The mean ACT score is 24.2 ( = 2.8); the mean of skipped is 1.1 ( = 1.08). The regression results in Stata format . reg co1GPA ACT skipped male 141 6.79 -0.0003 0.1294 Source df MS Number of obs Model 1 2.51207492 Residual 1 16.8940245 F(3, 137) 3 .837358308 Prob>F 137 .123314048 R-squared Adj R-squaredA 140 .138614996 Root MSE 35116 Total I 19.4060994 [95% Conf. Interval] 0117374 0538161 .0726537 Coef. Std. Err. t P> lt' B 0.002 skipped -.0949285 .0279197 -3.40 0.001 ACT 1 . 0327768 0106397 C -0.790.4301695006 male!-.0484234 cons I 2.392561 2541841 9.41 0.000 1.889929 2.895192 a. Fill in the five missing values in the highlighted spaces; note the corresponding letter (e.g. A) when you type your answers. b. Indicate which variables, if any, are statistically significant at the 95% level. Explain. c. Interpret each regression coefficient in words. Then discuss the magnitude of the estimated associations

Explanation / Answer

a.A) Adjusted R square = 1 – (1 – Rsquare)*(N – 1) / (N - p – 1)
                                          = 1 – (1 – 0.1294)*140/137 = 0.1103358
B) t-statistic = Coef / Std.Err = 0.0327768/0.0106397 = 3.080613
E) Std.Err = Coef / t stat = -0.0484234/-0.79 = 0.06129544
C) Confidence interval : Coeff ± t 0.025; 137 * Std.Err
Confidence interval = ( C= -0.1501378, D=-0.03971921)

b. ACT, SKIPPED and the constant are statistically significant since the p-value [ P > |t| ] is less than 5% indicating rejection of null hypothesis ( H0 : coefficient = 0 ).

c. Coeff(ACT) = 0.0327768 implies that there is an increase of 0.0327768 in College GPA if the ACT score is increased by 1 keeping all other variables constant.
Coeff(SKIPPED) = -0.0949285 implies that there is an decrease of 0.0949285 in College GPA if the avg. number of lectures skipped per week is increased by 1 keeping all other variables constant.
Coeff(MALE) = -0.0484234 implies that there is an decrease of 0.0484234 in College GPA if the gender is male keeping all other variables constant, else if gender is female, no change in college GPA.

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