Multiple Regression Model Assignment

Introduction:

In this assignment we are working on a retailer data set. The datasets pertain to an undisclosed business's online retail sales. Regrettably, due to the economic challenges stemming from the COVID-19 pandemic, the company has been compelled to reduce its workforce from 25 employees to just 5. Now, our objective is to conduct an in-depth analysis of the dataset to identify and assess the key factors that have had a significant impact on the business.

To check which factors are statistically significant for the sales. There are total five variables in the data set. The variables are described as follows:

Product type: The type of product sold in the retail store.
Net quantity: The number of products sold.
Gross sale: The total sales over the period
Discount: The amount of discount on a unit sold
Return: The money returned to the customer for unit that is returned
Net sales: Total sales after deduction of return amount from gross sale.

Note: There is no meaning to check the effect of gross sales on net sales as both variables measures the same.

First of all, we are doing the exploratory data analysis. We will generate some graphs to check variables are linearly correlated with the dependent variable net sales.

The check the distribution of the dependent variable.

We can see from the above that the unit sold variable has some sort of linear correlation with the net sales variable. The next variable gross sales obviously correlation with the net sales. The discount and returns variable have sort of negative correlation. This can be check using the correlation matrix. The correlation matrix is given as follows:

We can see from the above that dependent variable highly correlated with gross sales then discount followed by returns and net quantity.

Thus, we can say that there is sort of negative relationship between the net sales and discount and returns on the sold units. The higher the discount or return the lower the net sales.

To check the statistically significance of factors, the multiple regression is conducted as follows:

The above regression model is created, in the model the gross sales variable is not included because it is the same as the net sales variable just the returns are subtracted in the net sales. So, there is no logic to include the variable in the model.

The regression model created is as follows:

Net sales = 34.88 + 17.89 net quantity – 11.50 discount – 2.60 returns

The f-statistic for the model is 2617.91 with 0.00 p-value. The p-value is less than 5% so the model is significant model. Next, we will check for the significance for the slope variables. The slope estimate for net quantity is 17.89 indicates that with 1 unit increase in unit sold the net sales is increased by 17.89. The variable is statistically significant as the p-value is 0.00 that is less than 0.05.

The slope estimate for discount is -11.50 indicate that with 1 unit increase in the discount the net sales is decreases by 11.50. The variable is statistically significant as the p-value is 0.00 that is less than 0.05.

The slope estimate for returns is -2.60 indicate that with 1 unit increase in the return the net sales is decreases by 2.60. The variable is statistically significant as the p-value is 0.00 that is less than 0.05.

We can say that the model is good fit as total 81.60% variation in the dependent variable is explained by the independent variables.

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