Question

Following are the results from two different simple regression analyses estimating the costs of the marketing department using number of sales persons and number of units sold as cost drivers.

Variable	Coefficient	t-statistic	p-value
Intercept	500.75	4.05	0.03
Number of sales persons	20.50	6.10	0.004
Adjusted R-square = 0.80

Variable	Coefficient	t-statistic	p-value
Intercept	700.23	0.98	0.30
Number of units sold	120.33	3.66	0.05
Adjusted R-square = 0.49

a.   Which independent variable explains more of the variation in marketing department costs?

b.   Choose the most appropriate cost driver and write the cost function.

c.   What are the examples of uncertainties that could affect the accuracy of the cost function in estimating the cost for the next month.

Answer 1

Answer

(a)

Because the R-square value is higher, the 'number of salespersons' variable explains better.

(b)

The total marketing department cost would be the appropriate cost driver 500.75 +20.50 x numbers of sales persons.

(c)

Uncertainties can arise due to 1) input and 2) modeling

Example 1 - The input variable uncertainty can generate as the future number of salesperson may not be exactly known for the future. Even for the next month, some may leave the company, some may be on leave and so on. The exact value of the independent variable is uncertain.

Example 2 - The R-square value of 80% suggests that the 20% of the data is getting unexplained by the cost function prediction model. This is also a source of uncertainty.

Example 3 - The estimate is made from a sample data which may or may not represent the actual population data. So, the estimates are subject to the uncertainty that the whether the sample data is actually representing the population distribution of the variables.

Example 4 - Finally, we are assuming that the nature of the relationship of the future will exactly be same as that of the past. This is also uncertain. The model or the nature of the relationship between the variables can eventually change.