Question

Suppose a local car dealer is considering how to predict his weekly Quantity of Cars sold and he has hired you to conduct a regressionary analysis. He believes that the two key determinants of the demand is the number of salesmen on staff that week, and the hours the shop is open. Write out the Regression Equation and Interpret the intercept and the parameters on Hours and Salesmen. Determine if hours opened and salesmen are statistically significant variables in determining cars sold. Predict how many cars will be sold if the owner keeps his dealership open 56 hours a week and employs 10 salesmen?

From the equation which variables (salesmen or hours opened) appears to have the larger impact on sales? Justify your answer.

How much variation in cars sold do hours opened and salesmen explain?

Would you suggest altering this regression model to be modeled quadratically or in percent form? Yes or No – justify your answer either way. Or, might you consider adding another variable to this regression? What independent variable would you like to see tested in the regression?

Descriptive Statistics of Variables

Variable	Obs	Mean	Std. Dev.	Min	Max
Cars	935	35.744439	7.638788	12	56
Hours	935	43.92941	7.224256	20	80
Salesmen	935	13.46845	2.196654	9	18

Regression Results

Number of Observations = 935                 F-Ratio =86.70

R- squared = 0.4569                                    F-Ratio P-Value =0.000

Y = Cars	Parameter	Std. Err.	T- ratio	P- value	[95% Conf.	Interval]
Variables
Hours	0.183767	0.0319357	2.62	0.009	0.0210935	0.1464418
salesmen	1.324651	0.1050286	12.61	0.000	1.118531	1.530771
intercept	4.22352	1.913295	7.43	0.000	10.46866	17.97839

Answer 1

No, We can't comment on altering the regression model without the actual data as we first need to validate the assumption of linear regression before applying it. So, we would first need to check if the quadratic variable satisfies the assumption of linearity or not and then act accordingly. And as far as percentages are concerned, they would not bring any change to the model as you would be just changng the scale.

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We can definitely add more predictors to the regression model as these two variables only include 45.69% of variation in the number of cars sold per week.

We can add variables like 'Number of visiting customers per week' or 'Average time spent with a particular customer visiting'.