Statistics project

Journal article on Car Profits

Abstract

The article mainly discusses about the factors affecting car profit. Which we have identified are dealership size, sedan sales, and SUV sales. All these variables are positively related with the car profit of which dealership size has strong positive relationship with car profit. We have divided regression analysis in two model. Model one uses the independent variable dealership size only whereas model two uses the independent variable sedan sales and SUV sales as the function of profit.

1. Introduction

The purpose of this paper is to examine the effects of dealership size, sales of sedan, and sales of SUV on the car profit. Dealership size affects the sale of cars as bigger dealership size can store many cars both new and used. Similarly, the sales of sedan car and SUV also affect the car profit. We expect profit to be higher when there are higher sales. In this article, we are trying to see the magnitude of the dealership size and sales of vehicle.

This paper is expected to help businesses decide the weighed investment in various sector to increase profit. The profit on car is a function of dealership size, sedan sales, and SUV sales.

2. Methodology

we have taken the data of 10 dealer from across the country. This research begins with the descriptive analysis such as mean, median, variance, standard deviation, variance, and covariance. Also, we have done correlation analysis which helps us to see if there is any multicollinearity between the independent variables. Finally, we have conducted the linear and multiple regression analysis in excel. The significance of the derived equations is also checked using t-test, p-test, and F-test for each equation. The confidence level is set at 95%, i.e., α = 0.05.

Decision rule for significance:

Computed |F|, |T| > table value, reject the null hypothesis and

α > p-value, reject the null hypothesis

3. Empirical-Results

We, at first, try to summarize the data using the descriptive analysis and covariance. Looking at the covariance matrix, covariance between profit and sedan sales is 15271.6 which means they are positively related. Likewise, profit and dealership size are positively related as the covariance is 2838 which means when profit increases the dealership size and sedan sales also increases. On the other hand, profit and SUV sales are negatively related as their covariance is -1494.8 which means when profit goes higher the SUV sales goes down.

Also, the standard deviation for dealership size, sedan sales, SUV sales, and profit are 16.24, 110.36, 30.085, 199.51 respectively. Which means profit and sedan sales have higher variation than that of dealership size and SUV sales.

Here, I am trying to see if any multicollinearity exists between our independent variables and the relationship between these independent variables with the profit. Dealership size and profit have strong positive correlation. Similarly, SUV sales has weak negative relationship with profit and Sedan sales has moderate positive relationship with profit. For our second analysis, there exists no multicollinearity between SUV sales and sedan sales.

Table 1: Covariance

Table 2: Correlation

3.1 Regression Analysis

In the first analysis, I am trying to see the effects of dealership size on car profit. For this, I have performed the regression analysis in excel using the given dataset and divided the model in two model.

3.1.1 Model one:

If profit is affected by dealership size, the linear regression equation will be Y’ (Profits) = 8.17757206 + 11.94193141* Dealership size (in 1000 sq. ft)

(Please refer to excel output for the data)

I have defined my null and alternative hypothesis as follows:

Ho: β1 = 0 dealership size does not help to predict the car profit and

Ha: β1 ≠ 0. dealership size helps to predict the car profit

If the analysis fails to reject the null hypothesis, there is no relationship between profit of car and the size of dealership. On the other hand, if the analysis can reject the null hypothesis, there is linear relationship between profit of car and the dealership size. We reject the null if p-value is less than α. Also, if the computed t-value is greater than table t-value, we reject the null hypothesis.

The null hypothesis for this set of hypotheses is rejected as the p-value for dealership size is less than α, i.e., 0.000002.37 < 0.05. similarly, the calculated t-value (11.84391) for dealership is greater than table value (2.262). Moreover, we can say that the calculated equation is significant looking at F-value. Where in F table is 5.32 at 95% confidence level and the calculated F-value for the equation is 140.278249 which is greater than the table value. Therefore, we conclude that β1 ≠ 0 that means there is a linear relationship between car profit and size of dealership.

3.1.2 Model two:

Similarly, if profit is affected by the sales of sedan and SUV, the multiple linear regression equation will be

Y’ (Profits) = -504.869 + 2.257057 * sedan sales + 4.286976* SUV sales

At first, we check the significance of independent variables separately using P-value and t-Value.

Followings are the null and alternative hypothesis for this analysis: Ho: β1 = β2 = 0 None of the independent variables can predict the car profit

Ha: β1 ≠ β2 ≠ 0 At least one of the independent variables can predict the car profit

If the analysis can reject the null hypothesis, there is a linear relationship between at least one independent variable and car profit. Which means car profit is affected by sedan sales and SUV sales or sedan sales. If the analysis fails to reject the null hypothesis, there exist no linear relationship between dependent and independent variables.

At first, we are testing the significance of the equation by using F-test. The computed F value (12.65088) is greater than table (4.74). Therefore, we reject the null hypothesis. Which means the calculated equation is significant at 95% confidence level.

We also conduct the T-test to check significance of each independent variables. If the computed T-value for either of the variables is greater than that of table value, we reject the null hypothesis. The computed T-value for sedan sales and SUV sales is 4.777918 and 2.473776 whereas table T-value is 2.306 at 8 degrees of freedom at 95% confidence interval. Both computed T-values are greater than that of table value. Therefore, we conclude that both independent variables are significant to include in the equation.

Similarly, P-value for the sedan sales and SUV sales are 0.002017 and 0.042597 respectively. Both P-value are less than 0.05. That means both independent variables are significant in predicting car profit.

4. Discussion I suggest businesses to depend more on model one linear regression than model two multiple regression for couple reason. Let’s compare the adjusted R-squared and standard error of both equations. We would like to have greater adjusted R-squared and lower standard error to prefer one model over other. Higher R-squared means that the equation explains the higher variability. Whereas standard error of the regression provides the absolute measure of the typical distance that the data points fall from the regression line. Lower standard error means low variability in the data. Adjusted R-squared is 0.939303 and 0.721377 for model 1 and model 2 respectively. Similarly, the standard error is 49.15281 and 105.3111 for model 1 and 2 respectively. Therefore, model one is preferred over model 2. Model one explains 93.93% of the variability of the equation and the average distance of the observed value is 49.15 from the regression line. Whereas model 2 explains only 72.13% of the variability of the data and the average distance of the observed value is 105.31 from the regression line. Therefore, there are enough evidences to choose model one linear regression over multiple regression.

5. Conclusion

In this article we tried to examine the effect of dealership size, sedan sales, and SUV sales on car profit. We found that dealership size affects the most on car profit. If a dealership size increases by 1000 square feet, the car profit will be increased by $ 11941.93. Similarly, when a dealer sale a sedan, the profit will be increased by $ 2257.057. likewise, profit will be increased by $ 4286.976 when a dealer sale a SUV.

The stated hypothesis is rejected. Which means both the model are significant. Businesses can use both the model as a reference to increase profit. However, we suggest using the model one as it has low standard error and high R-squared.

Appendix

Pandey_Sabin_ECO 578_Fall_2019.xlsx