Question

3. Suppose we have a data set with five predictors, X1 = GPA, X2 = IQ, X3 = Gender (1 for Female and 0 for Male), X4 = Interaction between GPA and IQ, and X5 = Interaction between GPA and Gender. The response is starting salary after graduation in thousands of dollars). Suppose we use least squares to fit the model, and get Bo = 50, 8 = 20, B2 = 0.07, B3 = 35, B4 = 0.01, B5 = -10. (a) Which answer is correct, and why? i. For a fixed value of IQ and GPA, males earn more on average than females. ü. For a fixed value of IQ and GPA, females earn more on average than males. iii. For a fixed value of IQ and GPA, males earn more on average than females provided that the GPA is high enough. iv. For a fixed value of IQ and GPA, females earn more on average than males provided that the GPA is high enough. (b) Predict the salary of a female with IQ of 110 and a GPA of 4.0. (c) True or false: Since the coefficient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer.

Answer 1

Solutions Let, 1 X = GPA, z = Georden Here, The predicled multiple Seegersion equation, Y- 50 +20%, +0.07 Xg+ 3573 +0.0194 - 10.15 formale: Ym = 50+20%, +0:07 17 +35(0) +0.0194 -10(0) ûm - 50 +20%, +0:07 Ya+0.0124 for female: Ye - 50+ 20%, +0.07 4g + 35C1) torol Xy - 1015 19-85 +20 X, +0.07 1a +0.01 Xy -1015 B) option coii) is correct lie., For a fixed value of IQ and GPA, males Carn more on average than females provided that the GPA is high enough TQ = 110 and GPA-400 Ýs - 85+20x, +0.07 xq to-01 Xy û =8572004) +0:07(110) +0.01 ( 4X100) - 10C4x1)

Î. -85+80 + 707+4-4-40 The statement is false. Sence, . It also depends on standard error of beta estimates-