Term Paper on "Statistical Analysis With Regression"

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[EXCERPT] . . . .

Regression Analysis of Auto Sales

Statistical Analysis of Auto Sales

Eleven attributes all pertaining to the sales of automobiles sold from the first quarter of 1980 to the fourth quarter of 2004 form the data set and the basis of this analysis and the creation of a series of multiple regression models. The objective of the creation of a multiple regression equation is to predict sales of automobiles. Stepwise multiple regression was used, yielding the following models as shown in Table 1. Using stepwise regression the variable SPSS Version 13 for Windows' stepwise regression technique yielded Personal Income (pi) as the independent variable that most influenced sales of new autos (unitsales) and as a result the first model created includes only this variable. Finance Rate (finrate) was seen as the next most explanatory independent variable with the most influence on unitsales. The inclusion of finrate and pi leads to the second model. Adding in the index of the cost of car ownership (costcarown) produces a third model, and including consumer's overall sentiment comprises the fourth model. To see the combined effects of all other variables, finrate is taken from the fifth model. The sixth model includes the influence labor strikes have on the sales.

Table 1: Defined Statistical Models

Model

Variables Entered

Variables Removed

Method

Pi

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Finrate

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Costcarown

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Sentiment

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Finrate

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Strike

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Dependent Variable: unitsales

The strengths and weaknesses of each of these models are best defined by the level of correlation between each of the variables that comprise the regression equations. Table 2, Statistical Model Summaries, shows the specific R, R2 and Adjusted R2 values for each models' iteration.

Table 2: Statistical Model Summaries

Model RR Square Adjusted R. Square Std. Error of the Estimate Change Statistics Durbin-Watson R. Square Change F. Change df1 df2 Sig. F Change 1.624(a).389.378.9443.389 36.907 1-58.000 2.759(b).576.561.7932.187 25.198 1-57.000 3.824-.680.663.6956.104 18.109 1-56.000 4.876(d).768.751.5974.088 20.922 1-55.000 5.874(e).764.751.5975 -.004 1.018 1-55.317 6.893(f).797.782.5591.033 8.956 1-55.004 2.107 a Predictors: (Constant), pi

Predictors: (Constant), pi, finrate

Predictors: (Constant), pi, finrate, costcarown

Predictors: (Constant), pi, finrate, costcarown, sentiment

Predictors: (Constant), pi, costcarown, sentiment

Predictors: (Constant), pi, costcarown, sentiment, strike

Dependent Variable: unitsales

Notice the strength of each model's predictability increases with every successive inclusion of an independent variable, which translates into the successively higher R2 values as each model is computed. The exclusion of the variable finrate in model five makes little difference statistically, while the inclusion of this variable in addition to the variable strike lead to the highest levels of variability explained of all models, yielding an R2 of.782. This translates into 78% of the variance in auto sales during the sample period being explained by the variables included in these models.

The strengths and weaknesses of this model are clear: the greater the correlation as discovered by stepwise regression and introduced first into the analysis, the less significant the reduction in independent variables over time. Choosing the right independent variable to begin a stepwise regression is critical to the building of additional models and this is clearly seen the Table 2. Stepwise regression constraints defined for the model immediately lead to the variable personal income (pi) as being the foundation for the creation of multiple prediction models.

The weaknesses of this modeling approach include a lack of clarity on correlation between variables explored in greater depth using Pearson's Correlation Coefficient and 1-tailed Significance Tests. For the best results from regression analysis, a correlation matrix needs to be run first to ensure those variables that have the highest levels of collinearity are excluded and those with the highest R2 values that define the dependent variable of unitsales variability over time are included. The table, Appendix a: Correlation Matrix of all variables provides a correlation table for all 11 variables analyzed with both Pearson's Correlation Coefficient and 1-tailed Significance Tests. The stepwise regression analysis determined that personal income (pi), index of car ownership (costcarown), index of consumer sentiment (sentiment) and the likelihood of a strike (strike) when taken together explain 78% of the variation in unitsales. Looking now to… READ MORE

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