Question

Consider the simple linear regression model y=10+30x+e where the random error term is normally and independently distributed with mean zero and standard deviation 1. Do NOT use software. Generate a sample of eight observations, one each at the levels x= 10, 12, 14, 16, 18, 20, 22, and 24.

Do NOT use software!

(a) Fit the linear regression model by least squares and find the estimates of the slope and intercept.

(b) Find the estimate of ?^2 .

(c) Find the value of R^2.

(d) Do NOT use software. Generate a new sample of eight observations,
one each at the levels of x= 10, 14, 18, 22, 26, 30, 34, and 38. Fit the model using least squares.

(e) Find R2 for the new model in part (d). Compare this to the value obtained in part (c). What impact has the increase in the spread of the predictor variable x had on the value?

Answer 1

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.277236
R Square	0.07686
Adjusted R Square	-0.077
Standard Error	4.54204
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10.30591	10.30591	0.499556	0.506203
Residual	6	123.7808	20.63013
Total	7	134.0867
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	12.77821	6.169887	2.071061	0.083764	-2.31895	27.87538
x	0.247679	0.350426	0.706793	0.506203	-0.60978	1.10514

b) The estimate is 4.54*4.54=20.63

c)R square is 0.07686.