The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Which regression equation is best for predicting city fuel consumption? Why? Click the icon to view the table of regression equations. Choose the correct answer below. OA. The equation CITY=6.86-0.00131WT-0.258DISP+0.659HWY is best because it has a low P-value and the highest value of R². OB. The equation CITY=6.73 -0.00157WT +0.668HWY is best because it has a low P-value and the highest adjusted value of R². OC. The equation CITY = -3.15+0.823HWY is best because it has a low P-value and its R² and adjusted R² values are comparable to the R² and adjusted R² values of equations with more predictor variables. O D. The equation CITY=6.86 -0.00131WT-0.258DISP+0.659HWY is best because it uses all of the available predictor variables. - X Regression Table Predictor (x) Variables P-Value R² Adjusted R² Regression Equation WT/DISP/HWY 0.000 0.943 0.933 WT/DISP 0.000 0.748 0.720 WT/HWY 0.000 0.942 0.936 DISP/HWY 0.000 0.934 0.927 CITY=6.86-0.00131WT-0.258DISP+0.659HWY CITY = 38.4-0.00157WT-1.31DISP CITY=6.73-0.00157WT+0.668HWY CITY = 1.85-0.626DISP+0.702HWY CITY=41.8-0.00604WT CITY=29.4-2.96DISP CITY = -3.15+0.823HWY WT 0.000 0.713 0.698 DISP 0.000 0.659 0.641 HWY 0.000 0.924 0.920
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Which regression equation is best for predicting city fuel consumption? Why? Click the icon to view the table of regression equations. Choose the correct answer below. OA. The equation CITY=6.86-0.00131WT-0.258DISP+0.659HWY is best because it has a low P-value and the highest value of R². OB. The equation CITY=6.73 -0.00157WT +0.668HWY is best because it has a low P-value and the highest adjusted value of R². OC. The equation CITY = -3.15+0.823HWY is best because it has a low P-value and its R² and adjusted R² values are comparable to the R² and adjusted R² values of equations with more predictor variables. O D. The equation CITY=6.86 -0.00131WT-0.258DISP+0.659HWY is best because it uses all of the available predictor variables. - X Regression Table Predictor (x) Variables P-Value R² Adjusted R² Regression Equation WT/DISP/HWY 0.000 0.943 0.933 WT/DISP 0.000 0.748 0.720 WT/HWY 0.000 0.942 0.936 DISP/HWY 0.000 0.934 0.927 CITY=6.86-0.00131WT-0.258DISP+0.659HWY CITY = 38.4-0.00157WT-1.31DISP CITY=6.73-0.00157WT+0.668HWY CITY = 1.85-0.626DISP+0.702HWY CITY=41.8-0.00604WT CITY=29.4-2.96DISP CITY = -3.15+0.823HWY WT 0.000 0.713 0.698 DISP 0.000 0.659 0.641 HWY 0.000 0.924 0.920
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Transcribed Image Text:### Understanding Regression Analysis for Predicting Fuel Consumption
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal).
Which regression equation is best for predicting city fuel consumption? Let's analyze the results in detail.
#### Regression Table Analysis
The regression table provides several key metrics for different predictor variable combinations:
- **Predictor (x) Variables:** The combinations of predictors used in the regression equations.
- **P-Value:** Measures the significance of the predictors. A lower P-value suggests that the predictor is statistically significant.
- **R²:** Indicates the proportion of variance in the dependent variable that is predictable from the independent variables.
- **Adjusted R²:** Adjusted for the number of predictors in the model. It is a more accurate measure in the context of multiple regressors.
- **Regression Equation:** The regression coefficients for each predictor variable in the model.
Below is the detailed table as presented:
| Predictor (x) Variables | P-Value | R² | Adjusted R² | Regression Equation |
|-------------------------|---------|------|-------------|------------------------------------------------------|
| WT/DISP/HWY | 0.000 | 0.943| 0.933 | CITY = 6.86 - 0.00131WT - 0.258DISP + 0.659HWY |
| WT/DISP | 0.000 | 0.748| 0.720 | CITY = 3.84 - 0.00157WT - 1.31DISP |
| WT/HWY | 0.000 | 0.942| 0.936 | CITY = 6.73 - 0.00157WT + 0.668HWY |
| DISP/HWY | 0.000 | 0.934| 0.927 | CITY = 1.85 - 0.626DISP + 0.702HWY |
| WT | 0.000 | 0.713| 0.698 | CITY = 4.18 - 0.00604WT |
|
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