# Construct the indicated predic

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

 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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