The table below lists weights carats and prices dollars of r

The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. 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 a diamond that weighs 0.8 carats.

Weight

0.30

0.40

0.50

0.50

1.0

0.7

Price

$504

$1170

$1343

$1417

$5656

$2269

a. Find the explained variation [__]

(Round to the nearest whole number as needed.)

b. Find the unexplained variation [__]

(Round to the nearest whole number as needed.)

c. Find the indicated prediction interval. $[__]<y<$[__]

(Round to the nearest whole number as needed.)

Solution

Regression Analysis: price versus weight

Analysis of Variance

Source DF SS MS F P
Regression 1 16014570 16014570 58.18 0.002
Error 4 1101101 275275
Total 5 17115671

Model Summary

S R-sq R-sq(adj) R-sq(pred)
524.667 93.57% 91.96% 64.51%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -1991 573 -3.48 0.025
weight 7149 937 7.63 0.002 1.00

Regression Equation

price = -1991 + 7149 weight

a) explained variation=r²*var(price)=0.9357*3423134=3203026

b) unexplained variation=(1-r²)*var(price)=(1-0.9357)*3423134=220108

c) 95% prediction interval=(2041.44, 5414.50)=(2041,5415)