Question

For 5 students, scores on a math test (X) and statistics (Y) are given as follows:

X: 95 85 80 70 55

Y: 85 75 70 75 65

a) Fit the regression line b) Test the model c) Find the 90% Confidence Interval? d) For a student who has a math score 75, estimate her/his statistics grade?

Answer 1

Given Information:

Y	X
85	95
75	85
70	80
75	70
65	55

The regression analysis is performed in excel under Data Analysis at 10 percent level of significance and output obtained is:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.85115355
R Square	0.724462366
Adjusted R Square	0.632616487
Standard Error	4.495118818
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	159.3817204	159.3817204	7.887804878	0.0673751
Residual	3	60.61827957	20.20609319
Total	4	220
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	42.12365591	11.52651268	3.654501331	0.035380767	5.441148236	78.80616359	14.99758245	69.24972938
X Variable 1	0.413978495	0.147400753	2.808523612	0.0673751	-0.055116487	0.883073476	0.067090953	0.760866037

a) The fitted regression line is:

b) Since the pvalue for slope is 0.0673751 which is less than 0.10 and also the pvalue for intercept is 0.035380767 which is also less than 0.10. So the conclusion is null hypothesis is retained for both slope and intercept and they are not significant at 10 percent level of significance.

c) The 90% Confidence interval is shown below:

Confidence Interval	Lower 90.0%	Upper 90.0%
Intercept	14.99758245	69.24972938
Slope	0.067090953	0.760866037

d) For a student who has a math score 75, his/her estimated statistics grade is calculated as:

For a student who has a math score 75, his/her estimated statistics grade is 73.17204304