Question

A straight line is fitted to some data using least squares. Summary statistics are below. n=10, $\bar{x}=$5, $\bar{y}=$12, SSxx=142, SSxy=123, SSyy=155 The least squares intercept and slope are 7.65 and 0.87, respectively, and the ANOVA table is below.

Source	DF	SS	MS
Regression	1	106.54	106.54
Residual	8	48.46	6.06
Total	9	155

Compute a 95% confidence interval for the mean response when x=8.What is the critical value from the table? 2.3060 [1 pt(s)]

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Lower bound:  Upper bound:  [3 pt(s)]

Incorrect.

Tries 2/3

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Compute a 95% prediction interval for a new observation when x=8

Answer 1

95% confidence interval :

predcited value at X=8 is 7.65+8*0.87=		14.6100
std error confidence interval=		s*√(1/n+(x0-x̅)2/Sxx)		=	0.9950
for 95 % CI value of t=					2.3060
margin of error E=t*std error                            =					2.2945
lower confidence bound=sample mean-margin of error =					12.3155
Upper confidence bound=sample mean+margin of error=					16.9045

95% prediction interval:

std error prediction interval=		s*√(1+1/n+(x0-x̅)2/Sxx)		=	2.6552
for 95 % CI value of t=					2.3060
margin of error E=t*std error                            =					6.12
lower prediction bound=sample mean-margin of error =					8.4871
Upper prediction bound=sample mean+margin of error=					20.7329