Question

Two freshman algebra classes were studied, one of which used laptop computers at school and at home, while the other class did not. In each class, students were given a survey at the beginning and end of the semester, measuring his or her technological level. The scores were recorded for the end of semester survey (x) and the final examination (y) for the laptop group. The data and the MINITAB printout are shown here.

Student	Posttest	Final     Exam	Student	Posttest	Final   Exam
1	100	98	11	88	84
2	96	97	12	92	93
3	88	88	13	68	57
4	100	100	14	84	84
5	100	100	15	84	81
6	96	78	16	88	83
7	78	68	17	72	83
8	68	47	18	88	93
9	92	90	19	72	57
10	96	94	20	88	83

MINITAB output

Regression Analysis: y versus x
The regression equation is y = −26.9 + 1.26 x.
Predictor	Coef	SE Coef	T	P
Constant	-26.94	14.18	−1.90	0.074
x	1.2640	0.1621	7.80	0.000
S = 7.38366	R-Sq = 77.2%      R-Sq(adj) = 75.9%
Analysis of Variance
Source	DF	SS	MS	F	P
Regression	1	3316.5	3316.5	60.83	0.000
Residual Error	18	981.3	54.5
Total	19	4297.8

(a) Construct a scatterplot for the data. Does the assumption of linearity appear to be reasonable?

Yes, the assumption of linearity is reasonable. No, the assumption of linearity is not reasonable.    

(b) What is the equation of the regression line used for predicting final exam score as a function of the posttest score? (Round all numerical values to two decimal places.)
ŷ =

(c) Do the data present sufficient evidence to indicate that final exam score is linearly related to the posttest score? Use α = 0.01.

Yes, since the p-value is less than 0.01, there is sufficient evidence to indicate that final exam score is linearly related to the posttest score. Yes, since the p-value is more than 0.01, there is sufficient evidence to indicate that final exam score is linearly related to the posttest score.     No, since the p-value is less than 0.01, there is insufficient evidence to indicate that final exam score is linearly related to the posttest score. No, since the p-value is more than 0.01, there is insufficient evidence to indicate that final exam score is linearly related to the posttest score.

(d) Find a 99% confidence interval for the slope of the regression line. (Round your answers to three decimal places.)
to

Answer 1

A)

Final Exam 120 100 80 60 40 20 0 20 80 0 40 60 100 120

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8784
R Square	0.7717
Adjusted R Square	0.7590
Standard Error	7.3837
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3316.4690	3316.4690	60.8321	0.0000
Residual	18	981.3310	54.5184
Total	19	4297.8000
	Coefficients	Standard Error	t Stat	P-value	Lower 99.0%	Upper 99.0%
Intercept	-26.9411	14.1796	-1.9000	0.0736	-67.7561	13.8739
X Variable 1	1.2640	0.1621	7.7995	0.0000	0.7975	1.7305

y^ = -26.9411 + 1.2640 x

c)

p-value = 0.0000

p-value < alpha

hence the model is significant

option A) is correct

Yes, since the p-value is less than 0.01, there is sufficient evidence to indicate that final exam score is linearly related to the posttest score.

d)

99% confidence interval for slope =

0.798

1.730