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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). If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why? Click the icon to view the table of regression equations.

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). If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why? Click the icon to view the table of regression equations.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The table presented is a regression analysis summary, showcasing different predictor variables in relation to the dependent variable "CITY." Here's a detailed breakdown: | Predictor (x) Variables | P-Value | R² | Adjusted R² | Regression Equation | |-------------------------|---------|----|-------------|---------------------| | WT/DISP/HWY | 0.000 | 0.943 | 0.933 | CITY = 6.86 − 0.00133WT − 0.256DISP + 0.658HWY | | WT/DISP | 0.000 | 0.747 | 0.719 | CITY = 38.2 − 0.00164WT − 1.28DISP | | WT/HWY | 0.000 | 0.941 | 0.934 | CITY = 6.71 − 0.00164WT + 0.667HWY | | DISP/HWY | 0.000 | 0.935 | 0.928 | CITY = 1.88 − 0.624DISP + 0.702HWY | | WT | 0.000 | 0.711 | 0.696 | CITY = 41.5 − 0.00604WT | | DISP | 0.000 | 0.659 | 0.641 | CITY = 28.8 − 2.99DISP | | HWY | 0.000 | 0.924 | 0.920 | CITY = −3.11 + 0.823HWY | ### Explanation of Columns: - **Predictor (x) Variables:** Lists the independent variables used in the regression model. - **P-Value:** Indicates the statistical significance of the model. Values near 0 suggest a highly significant model. - **R² (R-squared):** Measures the proportion of the variance in the dependent variable that is predictable from the independent variables. - **Adjusted R²:** Similar to R² but adjusted for the number of predictors in the model, providing a more accurate measure for models with multiple variables. - **Regression Equation:** The mathematical equation derived from the regression analysis, showing how changes in predictor variables affect the dependent variable "CITY." This table offers insights into various predictive models using combinations of weight
Transcribed Image Text:The table presented is a regression analysis summary, showcasing different predictor variables in relation to the dependent variable "CITY." Here's a detailed breakdown: | Predictor (x) Variables | P-Value | R² | Adjusted R² | Regression Equation | |-------------------------|---------|----|-------------|---------------------| | WT/DISP/HWY | 0.000 | 0.943 | 0.933 | CITY = 6.86 − 0.00133WT − 0.256DISP + 0.658HWY | | WT/DISP | 0.000 | 0.747 | 0.719 | CITY = 38.2 − 0.00164WT − 1.28DISP | | WT/HWY | 0.000 | 0.941 | 0.934 | CITY = 6.71 − 0.00164WT + 0.667HWY | | DISP/HWY | 0.000 | 0.935 | 0.928 | CITY = 1.88 − 0.624DISP + 0.702HWY | | WT | 0.000 | 0.711 | 0.696 | CITY = 41.5 − 0.00604WT | | DISP | 0.000 | 0.659 | 0.641 | CITY = 28.8 − 2.99DISP | | HWY | 0.000 | 0.924 | 0.920 | CITY = −3.11 + 0.823HWY | ### Explanation of Columns: - **Predictor (x) Variables:** Lists the independent variables used in the regression model. - **P-Value:** Indicates the statistical significance of the model. Values near 0 suggest a highly significant model. - **R² (R-squared):** Measures the proportion of the variance in the dependent variable that is predictable from the independent variables. - **Adjusted R²:** Similar to R² but adjusted for the number of predictors in the model, providing a more accurate measure for models with multiple variables. - **Regression Equation:** The mathematical equation derived from the regression analysis, showing how changes in predictor variables affect the dependent variable "CITY." This table offers insights into various predictive models using combinations of weight
### Regression Analysis on Car Data 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 miles per gallon). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in miles per gallon). If only one predictor (x) variable is used to predict city fuel consumption, which single variable is best? Why? Click the icon to view the table of regression equations. --- #### Best Predictor Variable The best variable is **HWY** because it has the best combination of a **small** P-value, **0.000**, and a **large** adjusted \( R^2 \). (Type integers or decimals. Do not round.)
Transcribed Image Text:### Regression Analysis on Car Data 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 miles per gallon). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in miles per gallon). If only one predictor (x) variable is used to predict city fuel consumption, which single variable is best? Why? Click the icon to view the table of regression equations. --- #### Best Predictor Variable The best variable is **HWY** because it has the best combination of a **small** P-value, **0.000**, and a **large** adjusted \( R^2 \). (Type integers or decimals. Do not round.)
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