Statistics

METHODOLOGY

For concluding on the subject matter, I have collected the data from 10 different dealership across the state. Then we ran a linear regression on 3 different independent variables which are

a) Dealership Size

b) SUV sale

c) Sedan sale

Our dependent variable is profit as we are trying to determine the profit level based on these 3 independent variables. In order to do this, I used MICROSOFT EXCEL. Besides simple linear equation, I will also look at T-Stat, P-value as well as F-Value for the variables and equations. This will help in determining the significance of the model and the β coefficient.

I have divided the data set into 2 section for the analysis. For the 1st part, we will take dealership size as the determining factor for profit. Similarly on the 2nd part we will look at SUV sales and Sedan sales together as a determining factor of profit for dealership

1ST MODEL ON THE BASIS OF DEALERSHIP SIZE

ORDINARY LEAST SQUARES

Firstly, on my study I looked at if Profit was dependent on Dealership Size. After that, I ran the data on MICROSOFT EXCEL, and I found the regression equation as

Profit (Ŷ) = 8.1775 + 11.9419 (Dealership size)

SE = 49.15281

Adjusted R Square = 0.939303

R Square = 0.946047

From the above the equation, we can state that 1 unit increase in dealership size will lead to 11.9419 unit increase in profit for the dealership other things remaining constant.

R square for the equation is 0.946047 . This implies that 94.60 % of the variability is explained by the equation

In this analysis , I have set the following hypothesis

Ho:β1=0 Dealership size does not help predict profit i.e. Null Hypothesis

Hα:β1≠0 Dealership size help predict car profit i.e. Alternative hypothesis

In order to confirm the significance of the study, I did a F- test for the regression the condition is

Computed |F| value > Table F value we reject the null hypothesis. i.e. Ha:β1≠0

Computed |F| value ≯ Table F value we fail to reject the null hypothesis i.e. Ha:β1=0

Since, the values can be on either side of the numerical values, I will use a two tailed test. The computed F test = 140.2782 and Table F value (F0.05, 1, 8) = 5.32

140.2782 > 5.32 Reject Ho

From the above test, we can conclude that our model is statistically significant. In simple terms, we can confidently state that the dealership size can be used as an independent variable in order to determine the profit level for the dealership. This is further emphasized by R square which is 94.60 % implying that the model is statistically significant.

Therefore, Ho:β1≠0 is true

After stating that the model is statistically significant, I checked the significance of each coefficient. In our case, it is dealership size. To achieve this, we do a T-Test on the condition that :

Computed |T| value > Table T value we reject the null hypothesis.

Computed |T| value ≯ Table T value we fail to reject the null hypothesis.

From our excel regression sheet, we found that

Computed |T| value = 11.8439

Table value (T 0.05,9) = 2.2262

Since, Computed |T| > Table T value , we can confidently say that, the independent variable (Dealership Size) is statistically significant in the model.

After doing the T-Test , I also used P value to check the significance of the model on the condition that

α > Computed P value Reject the hypothesis

α ≯ Computed P value Fail to reject the hypothesis

In our case , α = 0.05 and Computed P value = 0.00000237. Thus we reject the hypothesis. This implies that the model is statistically significant.

2ND MODEL ON THE BASIS OF SUV SALES AND SEDAN SALES

Similarly, I also looked at whether SUV sales and Sedan sales were the determining factor for profit in the dealership. For this I took the same data set and ran a regression on it. After doing so I got the result as

Profit (Ŷ) = -504.869 + 2.257057 Sedan Sales + 4.286976 SUV sales

SE = 105.31106

R square = 0.783293

Adjusted R square = 0.721377

From the above equation, we can state that

1) Β1 = 2.257057. This means that 1 unit increase in Sedan sales will lead to 2.257057 units increase in profit for the dealership other things remaining constant

2) Β2 = 4.286976 . This means that 1 unit increase in SUV sales will lead to 4.286976 units increase in profit for the dealership other things remaining constant.

R square for the equation is 0.783293. This implies that 78.32 % of the variability is explained by the equation.

Like the first equation, in order to test the significance of our study, I have performed an F- Test on the equation. The hypothesis that I set is listed below

Ho: β1 ≠ β2 = 0 SUV sales and Sedan sale does not help to determine profit i.e. Null hypothesis

Ha: β1 ≠ β2 ≠ 0 SUV sale and sedan sale help determine profit i.e. Alternative hypothesis

From the regression equation, we see that the F value for the test i.e. Computed |F| value =12.6508

Table F value F(0.05, 2, 7) = 4.74

Like in the previous equation, our Computed |F| value > Table F value thus we reject the hypothesis which implies that our model is statistically significant. This is further explained by Adjusted R square which is 0.721377 which means that 72.13 % of the variability is explained by the model.

After, finding that our model is statistically significant, I checked the significance of each coefficient at 95% confidence. In our case they are SUV sales and Sedan Sales. To do this , we perform a T-Test on these variables on the condition that

Computed |T| value > Table T value we reject the null hypothesis.

Computed |T| value ≯ Table T value we fail to reject the null hypothesis.

FOR SEDAN SALES

Computed |T| value = 4.7791 and Table T value (0.05,8) = 2.306

Since 4.7791 > 2.306 , we reject the null hypothesis. i.e. Sedan sales is significant in the equation.

FOR SUV SALES

Computed |T| value = 2.4737 and Table T value (0.05,8) = 2.306

Since 2.4737 > 2.306 , we reject the null hypothesis. i.e. Sedan sales is significant in the equation.

After doing the T-Test , I also used P value to check the significance of the model and the variable on the condition that

α > Computed P value (Reject the hypothesis)

α ≯ Computed P value (Fail to reject the hypothesis)

FOR SEDAN SALES

In our case , α = 0.05 and Computed P value = 0.0020 , thus we can state that SEDAN SALES is significant in the model.

FOR SUV SALES

In our case , α = 0.05 and Computed P value = 0.0425 , thus we can state that SUV SALES is significant in the model.

Similarly, I also tried to see if any multicollinearity exists between the dependent and independent variables. In the table below, we can see that Dealership Size and profit has strong and a positive correlation. Whereas SUV sales has a negative and a weak correlation with profit and finally SEDAN sales has a moderate positive relationship with profit.

Furthermore, on the second analysis, I found that there was no any multicollinearity among SUV sales and sedan sales . This is shown in the table below.

EMPIRICIAL RESULTS

The use of descriptive statistics function was carried out in order to summarize the data. In the excel output, we can see that in the first model there is less variance for dealership size in relation to profit as compared to both SUV sales and Sedan sales. Same observation can be seen in terms of standard error. Similarly, the mean for dealership size is 37.5 whereas, the mean for SUV sales, Sedan sale for the dealership is 269.4 and 82.3 respectively.

DISCUSSUION

From the above calculation and data analysis, I conclude that in the vehicle dealership sector, all three of the selected independent variables play a certain role in determining the profit for the dealership. However, when business houses must select a model for their use , they should select the first model.

This is because, the first model i.e. Profit (Ŷ) = 8.1775 + 11.9419 (Dealership size) is explained a lot by descriptive statistics. Compared to the second equation, our preferred model has a higher Adjusted R Square. This model is further backed up by the fact that it has a lower Standard error as compared to the second equation. This factor is listed in the table below

CONCLUSION

In conclusion, we can state that our first model which focuses on dealership size plays an important role in determining the profit level for the dealership.

Furthermore, we can state that every dealership if they want to increase their profit level, they should focus as much as possible on their size. The simple reason might be the fact that when ever the size of the dealership is big, it attracts more and more customer. This in turn leads to increase in profit for the dealership. Having said that, not only dealership size but also SUV and Sedan Sales play an important role in determining the profit level for the dealership. But this factor is not statistically significant to the dealership size. This means that dealership should not fully focus on the dealership size but they should also focus on SUV Sales and Sedan Sales as well.

APPENDIX