Question

A study was conducted to determine whether the final grade of a student in an introductory psychology course, x, is linearly related to his or her performance on the verbal ability test administered before college entrance, y. The verbal scores and final grades for 1010 students are shown in the table below.

Student	Verbal Score	Final Grade
1	64	76
2	50	56
3	34	43
4	38	49
5	49	59
6	56	70
7	57	68
8	72	89
9	40	44
10	60	48

Find the following rounded to three decimal places.

Part a:
The correlation coefficient
SSx=
SSy=
SSxy=
r=

Part b:
The equation of the least squares regression line
y^= + x

Part c:
The predicted final grade of a student with a verbal score of 50


Part d:
Should the regression equation be used to predict the final grade of a student with a verbal score of 100? (Type: Yes or No .)


Part e:
The coefficient of determination
R2=

Answer 1

Solution:

a) correlation coefficient is:

2) The equation of lest square regression line:

c) for X=50 predict Y?

Y= 4.5529 + 1.0701X

Y= 4.5529 + 1.0701*50

Y= 58.06

d) Yes, we use the regression equation to predict final grades of students with verbal score of 100.

Y=4.5529 + 1.0701*100= 111.56

e) Coefficient of determination:

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