Journal Article on Profits

Journal Article

Sales and Dealership Size as a Predictor of a Store’s Profit

Abstract

This study aims to know if a dealership’s size and sales could affect the owner’s profit. The statistical analysis that was used is multiple linear regression analysis. The results showed that a dealership’s size can explain 94.46% of the owner’s profit. On the other hand, the sales in both Sedans and SUV’s can explain 79.26% of the owner’s profit. Other than that, the analysis also showed that the increase in dealership size by a thousand sq. ft can also increase the profit by 11 940. For the sales, an increase in Sedan sales by one could increase the profit by 2 320 and an increase in SUV sales by one could increase the profit by 4 790. All of the coefficients and the regression models are proven significant and reliable by using multiple hypothesis testing. By using these results, a person aspiring to be a retailer owner would know what to increase so that his/her profits would increase too.

SALES AND DEALERSHIP SIZE AS A PREDICTOR OF A STORE’S PROFIT

Establishing a store is easy because all that is needed is an initial investment and good management skills. The challenging task to do is making that store successful. There are many factors that could affect a store’s monthly profit. The mere design of a retailer, including color and interior design, can increase the owner’s profit. One measurable factor that could affect revenue is the owner’s initial investment. If the owner is willing to risk a lot, then the possible income would be more than that. In the end, knowing how much one factor can affect a store’s profit is a desirable trait. It can be achieved easily by using regression analysis in Microsoft Excel or SPSS. Getting the data is easy but interpreting the data can be difficult.

METHODOLOGY

Linear regression and multiple linear regression analysis are both thorough methods of determining correlation and determination. This is the statistical analysis used. By using Microsoft Excel’s Analyst Tool Pack, summary outputs of regression statistics and ANOVA was able to be gathered. The summary outputs are attached in the appendices. From those analyses, the equations for the predicted value of profit based on the independent variables were created. Other than the equations, their characteristics are also present, such as the standard error, t-stat, p-value, and F value. Standard error of a statistic is the standard deviation of the data, which uses sampling distribution (Everett). In regression, it is the standard error of the regression coefficient. P-value is the probability value for a given statistical data is the same or greater than the number of the observed (Wasserstein and Lazar). F value is used to compare the data that has been fitted to another data set to check if the sample can represent the population (Lomax). Lastly, the t-statistic is the proportion of how far the value of a restriction is from a computed value to its standard. It is a lot like the z score but it’s used when the sample size is less than 30 ("T Statistic: Definition, Types and Comparison to Z Score"). Before showing the results of the analysis, the initial data should be presented first. The units are in thousands square feet and in thousands.

Table 1: Data of a store showing their dealership size, profit, and sales which is categorized by type of car,

This is the data that was analyzed. The next two tables are the results.

This shows the result for the regression analysis when profit is the dependent variable and dealership size is the independent variable.

This shows the result for the regression analysis when profit is the dependent variable and Sedan sales and SUV sales are the independent variables.

EMPERICAL-RESULTS

Both of the situations show promising results. The very first data property needed is the significance-F. It shows how reliable the results are. To know how important the result is, with the use of significance-F, subtract is from one (1) and then multiply it to 100 and add a percentage symbol (%). The resulting number is the confidence level of how reliable the results are. Both of the equations show 99.99% confidence level.

The next data results are for the use of hypothesis testing. To test if the slopes of the equations are significant, the slope should not be equal to 0. Therefore, the null hypothesis is that the coefficient is equal to 0. For the coefficient to be considered significant, the null hypothesis should be rejected. For that to happen, the t-statistic from the results should be greater than the critical values from the t-table.

For the first equation, wherein the dealership size is the independent variable, this is the result.

Hypotheses:

Ho: β = 0

Ha: β ≠ 0

Decision: From the t distribution, df = 7 and α = 0.05, critical value is 2.365

11.84 > 2.365 Therefore, the Ho is rejected.

For the second equation, wherein the Sedan and SUV sales are the independent variables, this is the result.

Hypotheses:

Ho: β1 = B2 = 0

Ha: β1 ≠ β2 ≠ 0, or all three are not equal to 0.

Decision: From the t distribution, df = 7 and α = 0.05, critical value is 2.365

2.71 > 2.365 and 4.91 > 2.365 Therefore, the Ho is rejected.

To test if the regression models are significant, calculated F value should be greater than F critical, or the F value from a standard F-ratio table.

For the first equation, wherein the dealership size is the independent variable, this is the result.

Hypotheses:

Ho: the regression model does not explain any of the total variation in the dependent variable

Ha: the regression model does explain a proportion of the total variation in the dependent variable that is greater than 0

Decision: From the F-ratio table, regression df = 1 residual df = 8 and α = 0.05, F critical is 5.32

140.28 > 5.32 Therefore, the Ho is rejected.

For the second equation, wherein the Sedan and SUV sales are the independent variables, this is the result.

Hypotheses:

Ho: the regression model does not explain any of the total variation in the dependent variable

Ha: the regression model does explain a proportion of the total variation in the dependent variable that is greater than 0

Decision: From the F-ratio table, regression df = 2 residual df = 7 and α = 0.05, F critical is 4.74

13.36 > 4.74 Therefore, the Ho is rejected.

To test if the coefficients are significant, the P-value of an independent value should be less than the confidence level (α).

For the first equation, wherein the dealership size is the independent variable, this is the result.

Hypotheses:

Ho: β = 0

Ha: β ≠ 0

Decision: the confidence level α is 95% or 0.95.

2.36 × (10-6) < 0.05 Therefore, the Ho is rejected.

For the second equation, wherein the Sedan and SUV sales are the independent variables, this is the result.

Hypotheses:

Ho: β1 =2 = 0

Ha: β1 ≠ β2 ≠ 0, or all three are not equal to 0.

Decision: the confidence level is 95%, therefore α is 0.05

0.03 < 0.05

4.08 × (10-3) < 0.0.5 Therefore, the Ho is rejected.

Now that it has been proven that the regression models and their coefficients are significant, the thing to explain is how much do the regression models explain the data. The coefficient of determination, or R square, measures how much can the independent variable explain the value of the dependent variable. For the first equation, the R square is 0.9460. This means, that 94.60% of the difference in Dealership Size (X) can explain the Profit (Y) of a store. For the first equation, the R square is 0.7924. This means, that 79.24% of the difference in Sedan sales (X1) and SUV sales (X2) can explain the Profit (Y) of a store. They are both positive, this means that greater the dealership size, Sedan sales, and SUV sales are, the higher the profits would be.

DISCUSSION

According to the results, all of the determinants, given dealership size, Sedan sales, and SUV sales, can and will increase the profits of a store. But in this situation, the dealership size of a retailer is the most influential factor in the increase or decrease of their profit. The regression model wherein the dealership size is the independent variable is better than the regression model wherein the Sedan sales and the SUV sales are the independent variables. This is because the value of R square in the first situation is significantly greater than the latter. This means that the increase in dealership size can greatly affect the retailer’s profit. According to the equation, each 1000 sq. ft increase in the size of their dealership would also mean an increase in their profit by 11 940.

CONCLUSION

Using regression models in sales is very effective and important to boost in sales. In these situations, it has been evident that a dealership’s size and sales will greatly affect a dealer’s profit.

Appendices (Excel Workbook Copied)