Residuals: Min 10 Median 30 Маx -84.12 -27.18 10.61 36.90 48.26 Coefficients: Estimate Std. Errort value Pr(>[t|) (Intercept) 356.12083 197.17401 1.806 0.113859 xl -0.09874 0.04588 -2.152 0.068372 . x2 122.86721 21.79975 5.636 0.000786 *** --- Signif. codes: O **** 0.001 **' 0.01 *' 0.05 '.' 0.1 '' 1 Residual standard error: 51.14 on 7 degrees of freedom Multiple R-squared: F-statistic: 17.31 on 2 and 7 DF, 0.8318, Adjusted R-squared: p-value: 0.00195 0.7838 a. Determine the estimated regression equation that can be used to predict the price of a backpack given the capacity and the comfort rating. b. Interpret the model. c. Predict the price for a backpack with a capacity of 4500 cubic inches and a comfort rating of 4.

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Designers of backpacks use exotic material to make packs that fit comfortably and distribute  weight to eliminate pressure points. For fitting a regression model of price of backpack on the  capacity (cubic inches) and comfort rating of backpacks, a data for 10 backpacks are used.  Comfort was measured using a rating from 1 to 5, with a rating of 1 denoting average comfort  and a rating of 5 denoting excellent comfort. The output of the regression model is as follows on the next page:

 

 





Residuals:
Min
1Q Median
30
Маx
-84.12 -27.18
10.61
36.90
48.26
Coefficients:
Estimate Std. Error t value Pr (>[t])
(Intercept) 356.12083
197.17401
1.806 0.113859
xl
-0.09874
0.04588
-2.152 0.068372
x2
122.86721
21.79975
5.636 0.000786 ***
Signif. codes:
O *** 0.001
1**! 0.01
1*' 0.05 '.' 0.1 '' 1
Residual standard error: 51.14 on 7 degrees of freedom
Multiple R-squared:
0.8318,
Adjusted R-squared:
0.7838
F-statistic: 17.31 on 2 and 7 DF,
p-value: 0.00195
a. Determine the estimated regression equation that can be used to predict the price of a
backpack given the capacity and the comfort rating.
b. Interpret the model.
c. Predict the price for a backpack with a capacity of 4500 cubic inches and a comfort
rating of 4.
d. Comment on goodness of fit of the model.
Transcribed Image Text:Residuals: Min 1Q Median 30 Маx -84.12 -27.18 10.61 36.90 48.26 Coefficients: Estimate Std. Error t value Pr (>[t]) (Intercept) 356.12083 197.17401 1.806 0.113859 xl -0.09874 0.04588 -2.152 0.068372 x2 122.86721 21.79975 5.636 0.000786 *** Signif. codes: O *** 0.001 1**! 0.01 1*' 0.05 '.' 0.1 '' 1 Residual standard error: 51.14 on 7 degrees of freedom Multiple R-squared: 0.8318, Adjusted R-squared: 0.7838 F-statistic: 17.31 on 2 and 7 DF, p-value: 0.00195 a. Determine the estimated regression equation that can be used to predict the price of a backpack given the capacity and the comfort rating. b. Interpret the model. c. Predict the price for a backpack with a capacity of 4500 cubic inches and a comfort rating of 4. d. Comment on goodness of fit of the model.
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