Question

Student ID	Student ACT Score (Independent Variable)	Student            GPA     (Dependent Variable)
1	24	3.25
2	21	2.87
3	18	2.66
4	22	3.33
5	22	2.87
6	22	3.21
7	18	2.76
8	28	3.91
9	29	3.55
10	18	2.55
11	20	2.44
12	24	3.22
13	25	3.22
14	24	3.44
15	21	3.01
Instructions: Generate on a separate worksheet a standard set of SUMMARY OUTPUT for two-variable regression, and label the worksheet "Simple Regression Output". Then, using the information in this output 1) indicate whether there is a significant relationship between students' ACT scores and their GPAs, and 2) show the general prediction line (i.e., regression equation between these two variables), and 3) use this prediction line to compute the predicted GPA with an ACT score of 20.

Answer 1

SolutionA:

install analysis tool pak in excel

go to

data>data anlaysis>regression

select y as GPA

x as ACT

you will get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.88358236
R Square	0.780717786
Adjusted R Square	0.763849924
Standard Error	0.194760814
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.755646929	1.755646929	46.28433	1.26E-05
Residual	13	0.493113071	0.037931775
Total	14	2.24876
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.72177665	0.3511329	2.055565429	0.060486	-0.0368	1.480353161
Student ACT Score (Independent Variable)	0.105545685	0.015513989	6.803259071	1.26E-05	0.07203	0.13906162

Solutionb:

1) indicate whether there is a significant relationship between students' ACT scores and their GPAs,

t statistic for slope=6.803

p=0.000013

p<0.05

Reject H0

Accept Ha.

at 5% level of significance there is a significant relationship between students' ACT scores and their GPAs.

Solution2:

GPA=0.7218+0.1055*ACT

slope=0.1055

y intercept=0.7218

d 3) use this prediction line to compute the predicted GPA with an ACT score of 20.

For ACT=20 substitute in regression eq

GPA=0.7218+0.1055*ACT

GPA=0.7218+0.1055*20

= 2.8318

predicted GPA=2.8318