Question

Listed below are altitudes​ (thousands of​ feet) and outside air temperatures​ (°F) recorded during a flight. Find the​ (a) explained​ variation, (b) unexplained​ variation, and​ (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear​ correlation, so it is reasonable to use the regression equation when making predictions. For the prediction​ interval, use a​ 95% confidence level with the altitude of 6327 ft​ (or 6.327 thousand​ feet).

Altitude   Temperature
3   60
10   40
13   22
24   -5
28   -25
31   -41
33   -60

a. Find the explained variation.

b. Find the unexplained variation.

c. Use technology to construct the prediction interval.

Answer 1

a)

explained variation =SSR =                   'Σ(Ŷ-Y̅)2                 =

11313.786 (please take care of number of decimals)

b)

unexplained variation =SSE =Syy-(Sxy)2/Sxx=

289.642(please take care of number of decimals)

c)

predcited value at X=6.327:	50.97
std error prediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)=		8.9545
for 95 % CI value of t=			2.571
margin of error E=t*std error                            =		23.018
lower prediction bound=sample mean-margin of error =	27.947
Upper prediction bound=sample mean+margin of error=	73.984

prediction interval =(27.947 , 73.984)

(please take care of number of decimals)