Managerial Report: Finding the Best Car Value
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 portion.
Looking even further into this analysis, we find that the p-value corresponding to F = 72.3939 is .0000. .0000 is < α =.05, so if we were testing for significance with a 95% confidence interval, we would find that there is a significant overall relationship between these “dummy” dependent variables and cost/mile. Furthermore, if we look at the coefficients of ‘dummy’ variables, we see that one is nearly twice the other (see below). We can therefore make the rough inference that upscale sedans are more expensive to operate per-mile as family sedans.
II. Value Score vs. all Independent Variables
For the second part of this report, we ran a multiple regression analysis using Value Score as the dependent variable and Cost/Mile, Road-Test Score, Predicted Reliability, Family-Sedan, and Upscale-Sedan as the independent variables. The relevant portion of the analysis results are displayed below: Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.3779 0.1414 9.7469 0.0000 1.0933 1.6624 1.0933 1.6624
Family-Sedan 0.0238 0.0384 0.6194 0.5387 -0.0535 0.1011 -0.0535 0.1011
Upscale-Sedan 0.0678 0.0541 1.2520 0.2169 -0.0412 0.1767 -0.0412 0.1767
Cost/Mile -2.2715 0.1977 -11.4911
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 portion.
Looking even further into this analysis, we find that the p-value corresponding to F = 72.3939 is .0000. .0000 is < α =.05, so if we were testing for significance with a 95% confidence interval, we would find that there is a significant overall relationship between these “dummy” dependent variables and cost/mile. Furthermore, if we look at the coefficients of ‘dummy’ variables, we see that one is nearly twice the other (see below). We can therefore make the rough inference that upscale sedans are more expensive to operate per-mile as family sedans.
II. Value Score vs. all Independent Variables
For the second part of this report, we ran a multiple regression analysis using Value Score as the dependent variable and Cost/Mile, Road-Test Score, Predicted Reliability, Family-Sedan, and Upscale-Sedan as the independent variables. The relevant portion of the analysis results are displayed below: Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.3779 0.1414 9.7469 0.0000 1.0933 1.6624 1.0933 1.6624
Family-Sedan 0.0238 0.0384 0.6194 0.5387 -0.0535 0.1011 -0.0535 0.1011
Upscale-Sedan 0.0678 0.0541 1.2520 0.2169 -0.0412 0.1767 -0.0412 0.1767
Cost/Mile -2.2715 0.1977 -11.4911