Question

(267 points) Find the least-squares regression line û = bo + b1x through the points (-3,0),(2,8), (4, 15), (8, 18), (11,27), and then use it to find point estimates corresponding to x = 4 and x = = 8. For x = : 4, û = For x = 8, ĝ=

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.984968
R Square	0.970161
Adjusted R Square	0.960215
Standard Error	2.037057
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	404.7512	404.7512	97.53977	0.002207
Residual	3	12.44881	4.149602
Total	4	417.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5.423208	1.231009	4.405498	0.021691	1.505588	9.340829	1.505588	9.340829
X Variable 1	1.858362	0.188165	9.876222	0.002207	1.259536	2.457188	1.259536	2.457188

y = bo + b1X

$\hat{y} = 5.4232+ 1.8584X$

For x = 4, $\hat{y} = 5.4232+ 1.8584*4= 12.8566$

For x = 8, $\hat{y} = 5.4232+ 1.8584*8= 20.2901$