Finding the Best Car Value: Regression Analysis and Conclusions

This article discusses the regression analysis conducted to find the best car value based on various independent variables. The article includes four regression analyses and their results, including the best predictor of the value score of a car. The article concludes that the size of the car is not a good predictor of the value score of the car, and the value score of a car is best predicted using the road test score and cost per mile as the variables were statistically significant.

Running Header: Finding the Best Car Value 1
Finding the Best Car Value
Student’s name: Obaid Alshaali
Student’s ID:
Institution:

Finding the Best Car Value 2
1. Treating Cost/Mile as the dependent variable, develop an estimated regression with
Family-Sedan and Upscale-Sedan as the independent variables. Discuss your
findings.
Figure 1: Regression analysis
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.87
R Square 0.76
Adjusted R Square 0.75
Standard Error 0.05
Observations 54
ANOVA
df SS MS F Significance F
Regression 2 0.43 0.22 79.89 0.00
Residual 51 0.14 0.00
Total 53 0.57
Coefficients Standard Error t Stat P-value
Intercept 0.52 0.01 36.25 0.00
Family-sedan 0.12 0.02 6.42 0.00
Upscale-sedan 0.23 0.02 12.54 0.00
All factors kept constant, the base cost per mile of a car is 0.52. The base cost per mile is
statistically significant at p = 0.05. For a Family-Sedan, the cost per mile increases by 0.12 units.
On the other hand, for an upscale sedan, the cost per mile increases by 0.23 units.

Finding the Best Car Value 3
2. Treating Value Score as the dependent variable, develop an estimated regression
equation using Cost/Mile, Road-Test Score, Predicted Reliability, Family-Sedan and
Upscale-Sedan as the independent variables.
Figure 2: Regression analysis
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.97
R Square 0.94
Adjusted R Square 0.93
Standard Error 0.07
Observations 54
ANOVA
df SS MS F Significance F
Regression 5 3.60 0.72 138.81 0.00
Residual 48 0.25 0.01
Total 53 3.85
Coefficients Standard Error t Stat P-value
Intercept 1.37 0.14 9.82 0.00
Family-sedan 0.02 0.04 0.60 0.55
Upscale-Sedan 0.07 0.05 1.27 0.21
Cost/Mile -2.27 0.19 -11.69 0.00
Road-Test Score 0.01 0.00 8.48 0.00
Predicted Reliability 0.17 0.01 15.93 0.00
The regression equation that is derived from the regression model is:
Value_Score = 1.37 + 0.02Family-sedan + 0.07Upscale-sedan – 2.27Cost_mile +
0.01Road_Test_Score + 0.17Predicted_reliability

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3. Delete any independent variables that are not significant from the estimated
regression equation developed in part 2 using a .05 level of significance. After
deleting any independent variables that are not significant, develop a new estimated
regression equation.
Figure 3: Regression analysis 2
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.97
R Square 0.93
Adjusted R Square 0.93
Standard Error 0.07
Observations 54
ANOVA
df SS MS F Significance F
Regression 3 3.59 1.20 229.73 0.00
Residual 50 0.26 0.01
Total 53 3.85
Coefficients Standard Error t Stat P-value
Intercept 1.24 0.09 13.42 0.00
Cost/Mile -2.04 0.10 -19.51 0.00
Road-Test Score 0.01 0.00 9.25 0.00
Predicted Reliability 0.17 0.01 16.26 0.00
The new regression equation after deleting variables that are not significant is:
Value_Score = 1.24 – 2.04Cost_Mile + 0.01Road-Test_Score + 0.17Predicted_reliability
4. Suppose someone claims that “smaller cars provide better values than larger cars.”
For the data in this case, the Small Sedan represent the smallest type of car and the

Finding the Best Car Value 5
Upscale Sedan represent the largest type of car. Does your analysis support this
claim?
From the regression analysis in question 2 and 3, the model does not support the claim that
smaller cars provide better value than larger cars. The regression analysis has shown that the
variables based on Family-sedan and Upscale-sedan are not statistically significant. Value of a
car can only be judged on the basis of cost/mile, road-test score and predicted reliability.
5. Use regression analysis to develop an estimated regression that could be used to
predict the value score given the value of the Road-Test Score.
Figure 4: Regression analysis 3
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.19
R Square 0.04
Adjusted R Square 0.02
Standard Error 0.27
Observations 54
ANOVA
df SS MS F Significance F
Regression 1 0.14 0.14 2.03 0.16
Residual 52 3.70 0.07
Total 53 3.85
Coefficients Standard Error t Stat P-value
Intercept 0.90 0.32 2.83 0.01
Road-Test Score 0.01 0.00 1.43 0.16

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The regression equation derived from the regression model which aims to predict the value score
given the value of the Road-Test Score is:
Value_Score = 0.9 + 0.01Road_Test_Score
6. Use regression analysis to develop an estimated regression equation that could be
used to predict the value score given the Predicted Reliability.
Figure 4: Regression analysis 4
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.64
R Square 0.41
Adjusted R Square 0.40
Standard Error 0.21
Observations 54
ANOVA
df SS MS F Significance F
Regression 1 1.59 1.59 36.79 0.00
Residual 52 2.25 0.04
Total 53 3.85
Coefficients Standard Error t Stat P-value
Intercept 0.76 0.10 7.52 0.00
Predicted Reliability 0.17 0.03 6.07 0.00
From the regression model, the regression equation that was derived to predict the value score
given the predicted reliability is:
Value_Score = 0.76 + 0.17Predicted_Reliability
7. What conclusions can you derive from your analysis?

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From the analysis, it can be evident that the best predictor of the value score of a car is the
predicted reliability. The adjusted R squared is used to assess the best predictor when separate
regression models are constructed (Bates et al., 2014). The regression model, based on predicted
reliability as the independent variable has an adjusted R squared of 0.4. Thus, 40% of the
variability in the model is explained by factors in the model. Consequently, the value score of a
car is best predicted using the road test score and cost per mile as the variables were statistically
significant.
The size of the car is not a good predictor of the value score of the car. However, the size can be
used in determining the cost per mile of a car.

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Reference:
Bates, D., Maechler, M., Bolker, B., and Walker, S., 2014. lme4: Linear mixed-effects models
using Eigen and S4. R package version, 1(7), pp.1-23.