SPSS assignment

Question 1

Think about whether store size would have impact on weekly department sales. Form a hypothesis in your head or put it on paper. Now, run a linear regression to predict Weekly_Sales using tsize of store as the predictor. What is the R2 of the resulting model?

Hypothesis: Store size has positive, significant influence on weekly department sales.

For this analysis, the weekly sales is predicted by the number of stores and the returned R2 = 0.059. See details in SPV file.

Question 2

Think about whether unemployment would have an impact on sales at Walmart. Form a hypothesis in your head or write it down on a piece of paper. Now, run a linear regression to predict Weekly_Sales using unemployment as the independent variable. What is the R2 for the resulting model?

(Note: the p-value for the test of R2. If this results surprises you, as it should, think about why it is statistically significant).

Hypothesis: Unemployment has negative influence on weekly sales

For this analysis, the weekly sales is predicted with unemployment and obtained R2 = 0.001. See details in SPV file.

What the p-value imply is that the null hypothesis can either be accepted or rejected. In this case, p <0.05 and the null hypothesis is rejected and conclude that unemployment has negative influence on weekly sales.

Question 3

What is the impact of a 1% increase in unemployment rate on weekly department sales at Walmart?

Be sure to include the sign. Do not include units in your answer; only write the number. A positive sign would indicate an increase, while a negative sign would suggest a decrease.

One point (%) increase (change) in unemployment would result to -314.946 on weekly sales as documented in the “B” of unstandardized coefficients. See details in SPV file.

Question 4

What is the MAPE for this model?

The MAPE, which is also the MADE is represented in the regression coefficient table as standardized error. It is equal to 18.8 (approx.) percent. See details in SPV file.

Question 5

There are a large number of independent variables here. Assuming you don’t have a strong theoretical reason to include any particular variable in the model, you would use a statistical approach in selecting variables to include in the model. Run a stepwise variable selection method with the following independent variables: Size, IsHoliday, Temperature, Fuel_Price, CPI, and Unemployment. How many variables are included in the best model?

Six (6) variables. In this order: Predictors: (Constant), Size, CPI, Unemployment, Temperature, IsHoliday, Fuel_Price with Store Size as the best-fit variable.

Question 6

Now, do the same as above but using the forward variable selection method. How many variables are included in the best model?

The Six (6) variables are also included in the same manner as the Stepwise selection method. Predictors: (Constant), Size, CPI, Unemployment, Temperature, IsHoliday, Fuel_Price

Question 7

Repeat the above using the Backward method. How many variables are included in the best model?

All requested variables were entered.

Question 8

Now, run a model using the Enter method with the independent variable selected based on the Stepwise variable selection method. What is the R2 of this model?

(Think of how you could explain this result to your boss, CEO of Walmart.)

All the variables were entered in the Stepwise Method and as such entered in the Enter method. The R2 = 0.061.

The implication (explanation to the CEO) is that 61% of the total variation in the dependent variable can be explained by the independent variables

Question 9

What is the MAPE of this model?

(Think of what you would say to your boss, CEO of Walmart.)

Model		Unstandardized Coefficients
		B	Std. Error
1	(Constant)	8577.671	398.964
	IsHoliday	1398.830	134.506
	Size	.091	.001
	Temperature	29.142	1.956
	Fuel_Price	-454.467	76.847
	CPI	-18.800	.955
	Unemployment	-264.532	19.517

 

Based on the above table, the MAPE = sum of the standard error / number of variables

MAPE = 38.96

The implication of this is that the influence of 38.96 percent error gap should be applied in interpreting the influence of the independent variables on the dependent variables. However, this would be best understood through individual analysis as Size of store returned the most significant error margin (1%), showing that 99% of the influence that Size yields on Weekly Sales are correct and this goes for other variables.

Question 10

What is the RMSE of this model?

(Again, think of how you would explain this result to your boss, CEO of Walmar.)

In SPSS, RMSE is the same as the standard deviation and it is contained in the below table.

Descriptive Statistics
	Mean	Std. Deviation / RMSE	N
Weekly_Sales	15984.0260	22712.17621	421497
IsHoliday	.07	.256	421497
Size	136728.08	60980.976	421497
Temperature	60.0902	18.44753	421497
Fuel_Price	3.36103	.458511	421497
CPI	171.202288308	39.1594400648	421497
Unemployment	7.96021	1.863301	421497

 

The implication is that the RMSE explain the extent how the value differs from the middle (mean). For instance, in the case of Size, the RMSE is 60981 and this is because the different in middle is very vast.

Question 11

Which of the following is the second most important predictor of weekly department sales?

IsHoliday is the second most important with correlation of 0.013 (13 percent) as others had negative correlation