Final answer:
To identify good predictors of vehicle retail price, statistical methods such as multiple regression analysis are used. Variables with low p-values and high coefficients in the analysis could be considered significant. The slope in a regression between weight and fuel efficiency would show the expected change in efficiency per additional pound of weight.
Step-by-step explanation:
To determine which variables are good predictors of the retail price of a vehicle using the cars dataset, one would typically employ statistical methods such as regression analysis. The question seems to imply the use of multiple regression, where you would include the variables Drive Train, Origin, Cylinders, Vehicle Type, City Mileage, and Horsepower as independent variables in the model to test their predictive power on the dependent variable, which is the retail price. In conducting this analysis, you would collect the necessary data and then perform the regression. You would look at indicators such as R-squared values, p-values, and regression coefficients to determine the strength and significance of the relationship between each predictor and the retail price. A low p-value (typically less than 0.05) would suggest that the variable has a statistically significant effect on the price of the vehicle. Variables with significant p-values and larger standardized coefficients could be considered good predictors.
It's valuable to note that the relationship between weight and fuel efficiency could offer insights into the analysis. The practical interpretation of the slope in a least-squares regression line involving these two variables would tell you how much the fuel efficiency is expected to change for each additional pound of the car's weight. If you were to predict the fuel efficiency of a car that weighs 4,000 pounds, you would use the regression equation derived from your analysis. However, extending the prediction to a car that weighs 10,000 pounds could be unreliable if the data does not contain vehicles of such weight, as it would require extrapolation beyond the observed data range.