The Car Data Are Observations From Cars Selling On North Ame

The Car Data Are Observations From Cars Selling On North American Mark

The car data are observations from cars selling on the North American market. Five variables were collected for each car: Weight, Disp. (engine displacement in liters), Mileage, Fuel, and Type. The analysis involves fitting a multiple regression model with these variables, considering the appropriate SAS procedures and methods. This includes creating a new dataset excluding the "Type" variable to identify the best regression model using variable selection techniques.

Paper For Above instruction

Introduction

Understanding the factors that influence vehicle mileage is essential for manufacturers, consumers, and policymakers aiming to improve fuel efficiency and reduce emissions. The dataset in question comprises observations from various cars sold in North America, with variables including weight, engine displacement, mileage, fuel type, and vehicle classification (Type). This study seeks to model the relationship between mileage and other variables, first through a comprehensive model that incorporates the categorical variable 'Type' and then by refining the model after removing this variable to identify the most predictive set of continuous variables using variable selection techniques.

Part A: Regression Model with All Variables (Using PROC GLM)

The first step involves fitting a multiple linear regression model with Mileage as the dependent variable and Weight, Disp, Fuel, and Type as independent variables. Given that 'Type' is a categorical variable, the PROC GLM procedure in SAS is suitable because it can handle classification variables through the CLASS statement. The inclusion of 'Type' as a class variable allows SAS to generate the appropriate dummy variables automatically and partition the analysis accordingly. The code snippet for this analysis is as follows:



/ Importing the dataset - assuming data is in a text or CSV file, adapted as needed /


data cars;


infile 'path_to_datafile.csv' dlm=',' dsd firstobs=2;


input Name $20. Weight Disp Mileage Fuel $ Type $;


run;


/ Fit the regression model including the categorical variable 'Type' /


proc glm data=cars;


class Type;


model Mileage = Weight Disp Fuel Type;


run;

This model evaluates the effect of each predictor on mileage, accounting for the categorical nature of the 'Type' variable.

Part B: Model Without 'Type' and Variable Selection

Removing the 'Type' variable simplifies the dataset, leaving only continuous predictors: Weight, Disp, and Fuel. The goal here is to find the most predictive combination of these variables with respect to Mileage. The PROC REG procedure in SAS is appropriate for this task because it offers variable selection methods such as backward, forward, and stepwise selection. Using the 'SELECTION' option—specifically 'backward'—allows the model to iteratively eliminate the least significant variables, leading to an optimal subset based on statistical criteria such as AIC or SBC.

The code for this analysis is as follows:



/ Create a new dataset excluding the 'Type' variable /


data cars_no_type;


set cars;


drop Type;


run;


/ Fit the model with variable selection /


proc reg data=cars_no_type;


model Mileage = Weight Disp Fuel / selection=backward;


run;

Alternative options like forward and stepwise selection can be used similarly by replacing the 'selection=' parameter. These methods provide a systematic approach to identifying the most significant predictors for mileage, improving model interpretability and predictive accuracy.

Discussion and Interpretation

In the first model, including the categorical variable 'Type' enables a detailed analysis of how different vehicle classifications impact mileage, taking into account the specific characteristics associated with each type. The use of PROC GLM ensures proper handling of categorical predictors, facilitating the estimation of group differences and interactions if necessary. The coefficients from this model can inform manufacturers about the typical mileage implications of different car types while controlling for weight, displacement, and fuel type.

In the second analysis, removing the 'Type' variable shifts focus solely to the continuous predictors. Employing variable selection via PROC REG helps to identify which among weight, displacement, and fuel type most significantly influence mileage in the absence of classification effects. For instance, the backward selection method iteratively removes the least significant predictors, arriving at a parsimonious model that maintains predictive power. This approach simplifies understanding key physical and engineering factors affecting fuel efficiency, which can guide design improvements and consumer recommendations.

Conclusion

Modeling vehicle mileage based on physical and categorical attributes provides insights into factors that drive fuel economy. Using PROC GLM for models with categorical variables like 'Type' ensures proper statistical handling, while PROC REG with variable selection techniques effectively identifies the most critical continuous predictors. Combining these methods yields comprehensive insights into how vehicle characteristics influence fuel efficiency, aligning with industry and research objectives aimed at optimizing vehicle design and policy-making.

References

  • Fahrmeir, L., & Tutz, G. (2001). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer Series in Statistics.
  • Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani (2013). An Introduction to Statistical Learning. Springer.
  • Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S. Springer.
  • SAS Institute Inc. (2017). SAS/STAT® 14.3 User’s Guide. SAS Institute Inc.
  • Harrell, F. E. (2015). Regression Modeling Strategies. Springer.
  • Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley.
  • Faraway, J. J. (2002). Practical Regression and Anova using R. CRC Press.
  • Fox, J. (2015). Applied Regression Analysis and Generalized Linear Models. Sage Publications.
  • Chatterjee, S., & Hadi, A. S. (2015). Regression Analysis by Example. Wiley.
  • Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied Linear Statistical Models. McGraw-Hill.

Related Assignments