Question

1 76 (6 points) A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for all 10 students in the class are shown in the table below. Student Verbal Score x Final Grade y 34 78 2 56 3 76 68 4 34 76 5 33 60 6 49 98 7 45 65 8 41 71 9 67 10 69 96 62 Find the following (a) The correlation coefficient = (b) The least squares line y . (c) Calculate the residual for the fifth student BER

Answer 1

(a) Correlation coefficient(X, Y) = Cov(X, Y)/SD(X)SD(Y)

= $\sum (x - \bar x)(y - \bar y)/\sqrt{(\sum (x - \bar x)^2} \sqrt{(\sum (y - \bar y)^2}$

= 0.2187

(b) Performing regression between Y as dependent variable and X as independent variable, we get:

$\hat Y = 0.1795*X + 66.54$

(c) For 5th student, X = 33.

Predicted $\hat Y = 0.1795*33 + 66.54$ = 72.46

But actual Y = 60

Residual $e = Y - \hat Y$ = 60 - 72.46 = -12.46