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Construct the indicated predic

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January 18th, 2023

Construct the indicated prediction interval for an individualy.

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

SSE =Syy-(Sxy)2/Sxx= 13.4794
s2 =SSE/(n-2)= 2.6959
stderrorσ             = =se=√s2= 1.6419
x            = 14
predcitedvalue at X=14: 66.93
std errorprediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)= 1.8068
for 99 % CIvalue of t= 4.032
margin oferror E=t*stderror                           = 7.285
lowerprediction bound=sample mean-margin of error = 59.6490
Upperprediction bound=sample mean+margin of error= 74.2192

99% prediction interval =(59.6490 ,74.2192)

(please take care of number of decimalsrequired)

 
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