Managerial Report: Finding the Best Car Value
I. Cost/Mile vs. Car Size
Let us begin this report by examining how closely related Cost/Mile is to the Size of the car being tested. To do this, a multiple regression analysis was run using Cost/Mile as the dependent variable, and the ‘dummy’ variables Family-Sedan and Upscale-Sedan as independent variables.
In examining the results, the first thing we notice is the “R Square” value is 0.7471. This represents the multiple coefficient of determination (r2), which is basically a measure of goodness of fit of the equation estimated by the analysis. This means that the size of the car roughly accounts for 74.6% of the variance in the cost-per-mile of owning it—which is a rather large …show more content…
70 and 3 were chosen as the Road-Test Score and Predicted Reliability test-statistics, respectively. Using these values in all three test equations will ensure that we test only Cost/Mile (which we will treat as a representative of Size) with all other significant independent variables held constant. The values that we will use for Cost/Mile were found by calculating the average Cost/Mile for each of the three size categories (Small, Family, and Luxury). The resulting values were 0.52, 0.69, and 0.75, respectively.
Small Sedans = 1.252 – 2.0527(0.52) + 0.0113(70) + 0.1662(3) = 2.5416 – 1.0674 = 1.47
Family Sedans = 1.252 – 2.0527(0.69) + 0.0113(70) + 0.1662(3) = 2.5416 – 1.4164 = 1.13
Luxury Sedans = 1.252 – 2.0527(0.75) + 0.0113(70) + 0.1662(3) = 2.5416 – 1.5395 = 1.00
These estimated value scores, along with the already-discussed inference that (given this data) smaller cars cost less to drive per-mile, indicate that yes, smaller cars provide more value than larger cars—as their estimated value score (with all other variables constant) increases as the car size gets smaller.
V. Value Score vs. Road-Test Score
For the fifth part of this report, we will produce an estimated regression equation that could be used to predict the value score given the value of the Road-Test Score. To do this, first a multiple regression analysis with Value Score as the dependent variable, and Road-Test