The table below lists weights (carats) and prices (dollars) of randomly selected
ID: 3396020 • Letter: T
Question
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.)
Weight
0.30
0.40
0.50
0.50
1.0
0.7
Price
$504
$1170
$1343
$1417
$5656
$2269
Explanation / Answer
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)
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