Using the data on 1, 500 UAF students, the following equation was estimated by O

Question

Using the data on 1, 500 UAF students, the following equation was estimated by OLS: colgpa = 1.392 - 0.0135 hsperc + 0.001 48 sat n = 1, 500, R^2 = 0.073 where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top five percent of the class), and sat is the combined math and verbal scores on the student achievement test. (a) Interpret the intercept. Does it have a useful meaning? (b) Why does it make sense for the coefficient on hsperc to be negative? (c) What is the predicted college GPA when on hsperc = 21 and sat = 1100? (d) Suppose that two high school graduates, A and B, graduated in the same percentile from West Valley high school, but Student A's SAT score was 130 points higher (about one standard deviation in the sample). What is the predicted difference in college GPA for these two students? (e) Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa difference of 0.50, or one-half of a grade point? (f) Would you say hsperc and sat explain much of the variation in colgpa? Why or why not? Explain clearly.

Explanation / Answer

As per chegg policy, we are allowed to do only 4 parts.

a) The intercept is only left when all other independent variable are zero. The intercept (often labeled the constant) is the expected mean value of Y when all X=0. Start with a regression equation with one predictor, X. If X sometimes = 0, the intercept is simply the expectedmean value of Y at that value. The constant term (intercept) is in part estimated by the omission of predictors from a regression analysis. In essence, it serves as a garbage bin for any bias that is not accounted for by the terms in the model.

b) The lesser hsperc means the higher the student has scored. Thus, if hsperc is increased, his college gpa should also increase. To reflect that there is a negative sign.

c) hsperc = 21 and sat = 1100

colgpa = 1.392 - 0.0135 * 21 + 0.00148 * 1100

colgpa = 2.7365

d) hsperc for both students is same.

Let SAT score of A = 200

Then B's = 70

Colgpa of A - Colgpa of B = 1.392 - 0.0135 * hsperc + 0.00148 * 200 - (1.392 - 0.0135 * hsperc + 0.00148 * 70)

Colgpa of A - Colgpa of B = 0.00148 * 200 - 0.00148 * 70 = 0.1924

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