Consider the simple linear regression model y 10 30x E wh

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. Use software to generate a sample of eight observations, one each at the levels x = 10, 12, 14, 16, 18, 20, 22, and 24. (a) Fit the linear regression model by least squares and find the estimates for the slope and intercept. (b) Find the estimate for sigma^2 (c) Find the value of R^2.

Solution

a)

b) The estimate is 4.54*4.54=20.63

c)R square is 0.07686.

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