Table 11.24 shows results of fitting various regression models to data on y = college GPA, x1 = high school GPA, x2 = mathematics entrance exam score, and x3 =

verbal entrance exam score. Indicate which of the following statements are false. Give a reason for your answer.

TABLE 11.24 Model Estimates E(y) =

α + βx1 E(y) =

α+β1x1+β2x2 E(y) = α+β1x1

+ β2x2 + β3x3 Coefficient of x1 0.450 0.400 0.340 Coefficient of x2 0.003 0.002 Coefficient of x3 0.002 R2 0.25 0.34 0.38

(a) The correlation between y and x1 is positive.

(b) A one-unit increase in x1 corresponds to a change of 0.45 in the estimated mean of y, controlling for x2 and x3.

(c) In the third model, x1 has the strongest partial effect on y.

(d) The value of r2 yx3 is 0.40.

(e) The partial correlation ryx1·x2 is positive.

(f) Controlling for x1, a 100-unit increase in x2 corresponds to a predicted increase of 0.3 in college GPA.

(g) For the first model, the estimated standardized regression coefficient equals 0.50.