Question

Construct the indicated prediction interval for an individual y.

The equation of the regression line for the paired data below is \hat{y}=6.1829+4.3394x and the standard error of estimate is se=1.6419.

Find the 99% prediction interval of y for x=14.

x: 9 7 2 3 4 22 17

y: 43 35 16 21 23 102 81

Answer 1

SSE =Syy-(Sxy)2/Sxx=

13.4794

	s2 =SSE/(n-2)=	2.6959
std error σ              =	=se =√s2=	1.6419

x             =	14
predcited value at X=14:		66.93
std error prediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)=				1.8068
for 99 % CI value of t=				4.032
margin of error E=t*std error                            =				7.285
lower prediction bound=sample mean-margin of error =				59.6490
Upper prediction bound=sample mean+margin of error=				74.2192

99% prediction interval =(59.6490 , 74.2192)

(please take care of number of decimals required)