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

Regression Analysis
	r²	0.724
	r	0.851
	Std. Error	4.495
	n	5
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	159.3817	1	159.3817	7.89	.0674
Residual	60.6183	3	20.2061
Total	220.0000	4
Regression output				confidence interval
variables	coefficients	std. error	t (df=3)	p-value	90% lower	90% upper
Intercept	42.1237	11.53	3.65	0.04	15.00	69.25
x	0.4140	0.1474	2.809	.0674	0.0671	0.7609
Predicted values for: y
		90% Confidence Interval	90% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
75	73.172	68.391	77.954	61.563	84.781	0.204

a) Fit the regression line

y= 42.1237+0.4140x

b) Test the model

Since P value=0.0674>alpha(0.10) . We fail to reject the null hypothesis.

c) Find the 90% Confidence Interval?

(0.0671,0.7609)

d) For a student who has a math score 75, estimate her/his statistics grade?

73.172