Question

(1 point) 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 49 77 51 67 69 81 61 61 47 62 73 41 59 90 65 82 26 99 10 61 67 Find the following: (a) The correlation coefficient: r = (b) The least squares line: û = (c) Calculate the residual for the fourth student:

Answer 1

The statistic software output for this problem is:

Simple linear regression results: Dependent Variable: y Independent Variable: x y = 111.83667 -0.84889323 x Sample size: 10 R (correlation coefficient) = -0.41014366 R-sq=0.16821782 Estimate of error standard deviation: 25.255941

77 81 69 61 62 73 0 82 99 67 Residuals 6.759095 12.456882 14.039173 0.94581384 9.9386914 4.0320508 -61.751973 25.341387 9.2345507 6.9458138

(a)

r = -0.4101

(b)

$\hat y$ = 111.8367 - 0.8489 x

(c)

Residual for the fourth student = 0.9458