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Grade point average. The director of admissions of a small college seleeted 120 students at random from the new freshman class in a study to determine whether a students grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X) The results of the study follow. Assume that first-order regression model (1.1) is appropriate. 2 118 119 120 i: Xi: 21 Yi: 14 28 28 16 28 3.897 3.885 3.778.. 3.914 1.860 2.948 a. Obtain the least squares estimates of Po and B1, and state the estimated regression function. b. Plot the estimated regression function and the data. Does the estimated regression function appear to fit the data well? c. Obtain a point estimate of the mean freshman GPA for students with ACT test score X- 30. d. What is the point estimate of the change in the mean response when the entrance test score increases by one point?

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Assu me thut Trot-o>del model 〈,ו) s egression 別cute , 2 12 O Xi 2.8_.. 28 28 3.314 1-86o 2-juF om the Aiven dleex bi usin fx cEL Softuure, K) The leo+ squcure estimates of Po cY oe o. 0.3 gog and 2.לות respectively . Hore the valie of Ro.o 893 lou Thus the estmcted eession appears to nott the da el Aunct 〈 〉The Poîn testimate of X-30 1S x3 hem Y -3.837 jis the pointSom imes incteajes aS compare 4o Previous and Some 4ime de ceease s hus the change in mean Square incteae is lende

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