Truck
Maintenance Expense Miles Driven
1
$930.32
10550 10
2
$762.88
9750
7
3
$805.31
9250
8
4
$631.37
8350
9
5
$391.87
6550
5
6
$382.48
4550
2
7
$247.08
3550
2
8
$186.69
2250
3
9
$268.06
1850
2
Age of Truck (Years)
Using the above Truck fleet data including maintenance $, Mileage, and Truck age to address the
following:
Perform a Multiple Regression Analysis of the provided data (maintenance expense, mileage and
age).
a) Yes or No; is there an overall relationship between the maintenance expense of the Van and the
predictor variable of mileage and age?
b) Justify your answer to (a)
c) Is the current model parsimonious? Why or Why not?
d) What is the most parsimonious model? Jusitfy your response.
Note: A Regression Analysis is required of the most parsimonious model. Justification must include
output metrics to explain your decision.
ChatGPT
Unfortunately, as an AI language model, I can't directly perform a regression analysis because I don't
have the ability to compute on data. However, I can certainly guide you on how to do it and discuss
the expected findings.
Here's how you would perform a multiple regression analysis on the data:
Define your dependent variable (Maintenance Expense) and independent variables (Miles Driven
and Age of Truck).
Use a statistics software (like Python's statsmodels, R's lm, SPSS, etc.) to fit a multiple regression
model to your data. The software will output a table of coefficients for each independent variable, as
well as an overall F-statistic and associated p-value.
Here's how you could answer the given questions:
a) The overall relationship between the maintenance expense and the predictor variables can be
determined by looking at the F-statistic and the associated p-value. If the p-value is less than 0.05,
you would conclude that there is a statistically significant relationship between the predictors and
the response variable, and answer "Yes". If the p-value is not less than 0.05, you would conclude that
there is not a statistically significant relationship, and answer "No".
b) You justify your answer by referring to the p-value of the F-statistic. If the p-value is less than
0.05, this indicates that at least one of the predictors is significantly related to the response variable.
c) Parsimony in model selection refers to the idea that simpler models are better, as long as they
explain the data nearly as well as more complicated models. Whether the current model is
parsimonious depends on whether both predictors are significantly related to the response variable.
If both predictors are significant, the model is parsimonious because all included variables are
necessary. If one of the predictors is not significant, the model is not parsimonious because it
includes unnecessary complexity.
d) The most parsimonious model would be one that uses the fewest predictors while still explaining
the data well. To find this model, you could look at the p-values of the coefficients for the individual
predictors in your model. If one of the predictors has a p-value greater than 0.05, you might consider
removing it from the model.
After removing the less significant predictor, you would perform another regression analysis and
look at the R-squared value, which tells you the proportion of the variance in the response variable
that can be explained by the predictors. If the R-squared value is not much lower in the simpler
model, you might conclude that the simpler model is the most parsimonious.
Again, this is a general guide. You would need to actually perform the analysis using statistical
software and then interpret the output to answer these questions for your specific dataset.