1. Data was collected on 82 vehicles of different models to study the relationship between the weight of a vehicle (wt) and the miles per gallon (mpg) of the vehicle. The output from a regression analysis of the data is attached to the end of the sheet. a)Use the estimated linear regression model for predicting miles per gallon from weight to predict the miles per gallon for a vehicle with a weight of 40. b)Given that the mean weight of vehicles in the sample was 30.9, and that the corrected sum of squares (Sxx ) for weight was 5369., compute an interval estimate of the miles per gallon for an individual vehicle with a weight of 40. c) Here is a listing for a subset of the vehicle data: mpg wt 40.9 22.5 38.4 25.0 33.2 30.0 31.4 30.0 23.6 40.0 19.5 45.0 For this subset of the data, list the Y and X matrices that would be used in the matrix-based approach to regression for predicting miles per gallon from weight. Assume that the simple linear regression model yi = B0 + B1xi + ei used. d) For the vehicle data, what is the correlation coefficient value between weight and miles per gallon?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
Section11.2: Box-and-whisker Plots
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1. Data was collected on 82 vehicles of different models to study the relationship between the weight of a vehicle (wt) and the miles per gallon (mpg) of the vehicle. The output from a regression analysis of the data is attached to the end of the sheet.

a)Use the estimated linear regression model for predicting miles per gallon from weight to predict the miles per gallon for a vehicle with a weight of 40.

b)Given that the mean weight of vehicles in the sample was 30.9, and that the corrected sum of squares (Sxx ) for weight was 5369., compute an interval estimate of the miles per gallon for an individual vehicle with a weight of 40.

c) Here is a listing for a subset of the vehicle data:

mpg wt
40.9 22.5
38.4 25.0
33.2 30.0
31.4 30.0
23.6 40.0
19.5 45.0

For this subset of the data, list the Y and X matrices that would be used in the matrix-based approach to regression for predicting miles per gallon from weight. Assume that the simple linear regression model yi = B0 + B1xi + ei used.

d) For the vehicle data, what is the correlation coefficient value between weight and miles per gallon?

Source
Model
Error
Corrected Total
Results for the vehicle data analysis
Dependent Variable: mpg
Analysis of Variance
Sum of
Root MSE
Dependent Mean
Coeff Var
DF Squares
Square F Value Pr > F
1 6641.46093 6641.46093 362.43 <.0001
80
1466.00163
18.32502
81 8107.46256
Mean
4.28077 R-Square 0.8192
12.67187
The REG Procedure
33.78171 Adj R-Sq 0.8169
Parameter Estimates
Parameter Standard
Variable DF Estimate
Intercept 1 68.16545
wt
1 -1.11222
Error t Value Pr> |t|
1.86695 36.51 <.0001
0.05842 -19.04 <.0001
Transcribed Image Text:Source Model Error Corrected Total Results for the vehicle data analysis Dependent Variable: mpg Analysis of Variance Sum of Root MSE Dependent Mean Coeff Var DF Squares Square F Value Pr > F 1 6641.46093 6641.46093 362.43 <.0001 80 1466.00163 18.32502 81 8107.46256 Mean 4.28077 R-Square 0.8192 12.67187 The REG Procedure 33.78171 Adj R-Sq 0.8169 Parameter Estimates Parameter Standard Variable DF Estimate Intercept 1 68.16545 wt 1 -1.11222 Error t Value Pr> |t| 1.86695 36.51 <.0001 0.05842 -19.04 <.0001
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