Question

In: Statistics and Probability

A study was conducted to determine whether the final grade of a student in an introductory...

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 1010 students in the class are shown in the table below.

Student Verbal Score xx Final Grade yy
11 4242 8282
22 2626 7575
33 4747 7171
44 7272 7373
55 6565 9494
66 3737 7676
77 7777 9999
88 6060 6565
99 6262 7979
1010 7474 9393


Find the following:

(a) The correlation coefficient: r=r=

(b) The least squares line: y^=y^=

(c) Calculate the residual for the tenth student:

Solutions

Expert Solution

Answer a)

The correlation coefficient: r = 0.4940

Answer b)

The least squares line: y = 62.773 + 0.319*x

Answer c)

At x = 74, we get:

y = 62.773 + 0.319*74

y = 86.379

Residual = Observed value - Predicted value

Residual = 93 - 86.379

Residual = 6.621


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