Question

True Fit operates a chain of 10 retail department stores. Each department store makes its own purchasing decisions.

Haulton ,assistant to the president of True Fit ,is interested in better understanding the drivers of purchasing department costs. For many years,True Fithas allocated purchasing department costs to products on the basis of the dollar value of merchandise purchased. A $100 item is allocated 10 times as many overhead costs associated with the purchasing department as a $10 item. Haulton recently attended a seminar titled "Cost Drivers in the Retail Industry." In a presentation at the seminar,Sunshine Fabrics, a leading competitor that has implemented activity-based costing, reported number of purchase orders and number of suppliers to be the two most important cost drivers of purchasing department costs. The dollar value of merchandise purchased in each purchase order was not found to be a significant cost driver.

Haultoninterviewed several members of the purchasing department at theTrue Fitstore in Miami. They believed that Sunshine Fabrics' conclusions also applied to their purchasing department.Haulton

collects the following data for the most recent year for True Fit 's

10 retail department stores and performs simple regressions:

	Purchasing	Dollar Value of	Number of	Number
	Department	Merchandise	Purchase Orders	of Suppliers
Department Store	Costs (PDC)	Purchased (MP$)	(No. of POs)	(No. of Ss)
Baltimore	$1,523,000	$68,315,000	4,357	132
Chicago	1,100,000	33,456,000	2,550	222
Los Angeles	547,000	121,160,000	1,433	11
Miami	2,049,000	119,566,000	5,944	190
New York	1,056,000	33,505,000	2,793	23
Phoenix	529,000	29,854,000	1,327	33
Seattle	1,538,000	102,875,000	7,586	104
St. Louis	1,754,000	38,674,000	3,617	119
Toronto	1,612,000	139,312,000	1,707	208
Vancouver	1,257,000	130,944,000	4,731	201

Haulton decides to use simple regression analysis to examine whether one or more of three variables (the last three columns in the table) are cost drivers of Purchasing Department costs.

Regression 1:

PDC=a + (b x MP$)

Variable				Coefficient	Standard Error	t-Value
Constant				$1,039,061	$343,439	3.03
Independent variable 1: MP$				0.0031	0.0037	0.84

r squared=0.080.08 ; Durbin-Watson statistic=2.412.41

Regression 2:

PDC=a + (bx No. of POs)

Variable				Coefficient	Standard Error	t-Value
Constant				$730,716	$265,419	2.75
Independent variable 1: No. of POs				$156.97	$64.69	2.43

r squared=0.420.42 ; Durbin-Watson statistice=1.981.98

Regression 3:

PDCequals=aplus+ (b x No. of Ss)

Variable				Coefficient	Standard Error	t-Value
Constant				$814,862	$247,821	3.29
Independent variable 1: No. of Ss				$3,875	$1,697	2.28

r squared=0.390.39 ; Durbin-Watson statistic=1.97

He finds the following results for two multiple regression analyses:

Regression 4:

PDC=a + (b 1b1x No. of POs) + (b 2b2 x No. of Ss)

Variable				Coefficient	Standard Error	t-Value
Constant				$485,384	$257,477	1.89
Independent variable 1: No. of POs				$123.22	$57.69	2.14
Independent variable 2: No. of Ss				$2,952	$1,476	2.00

r squared=0.630.63 ; Durbin-Watson statistic=1.90

Regression 5: PDC=a+ (b 1b1 x No. of POs) + (b 2b2 x No. of Ss) + (b 3b3 x MP$)

Variable				Coefficient	Standard Error	t-Value
Constant				$494,684	$310,205	1.59
Independent variable 1: No. of POs				$124.05	$63.49	1.95
Independent variable 2: No. of Ss				$2,984	$1,622	1.84
Independent variable 3: MP$				0.0002	0.0030	0.07

r squared =0.63; Durbin-Watson statisticequals=1.90

The coefficients of correlation between combinations of pairs of the variables are as follows:

	PDC	MP$	No. of POs
MP$	0.29
No. of POs	0.65	0.27
No. of Ss	0.63	0.34	0.29

Requirement 1. Evaluate regression 4 using the criteria of economic plausibility, goodness of fit, significance of independent variables, and specification analysis. Compare regression 4 with regressions 2 and 3. Which one of these models would you recommend that Haulton

use? Why?

Let's begin by evaluating regression 4 using the criteria of economic plausibility, goodness of fit, significance of independent variables and specification analysis.

Regression 4
Economic plausibility (Plausible/non-plausible?)
Goodness of fit (excellent or poor fit?)
Significance of independent variables (insignificant or significant?)
Specification analysis (reject or not reject?)

Requirement 2. Compare regression 5 with regression 4. Which one of these models would you recommend that them to ​use? Why?

Answer 1

Requirement 1:

For Regression 4:

Economic Plausibility:

As there is a positive relationship (since the parameter estimates are positive) for the variables 'No. of Purchase Orders' and 'No. of Suppliers' with the dependent variable 'Purchasing Department Costs' the relationship is economically plausible.

Goodness of fit:

R-square is the proportion of variation in the dependent variable, explained by the explanatory variables is commonly described as a measure of goodness of fit.

Here R-square = 63% (=0.63*100) is an excellent fit

Significance of independent variables:

t-critical value at 10% significance level and 9 (=10-1) degrees of freedom = 1.833 (for a two-tail test)

Since the calculated t (= 2.14) > t-critical (=1.833) we infer that the independent variable 'No. of Purchase Orders' is significant

Since the calculated t (= 2.00) > t-critical (=1.833) we infer that the independent variable 'No. of Suppliers' is significant

Specification analysis:

Considering Durbin-Watson (DW) Statistic, d = 1.90

From the critical table of DW at n = 10 and k = 2;

d_L = 0.466 and d_U = 1.333

Since the calculated d (= 1.90) > d_U (= 1.333) we do not reject H₀

Considering the 'goodness of fit' measure of the three regression models, regression 2 (= 42%) and regression 3 (=39%) are lesser than regression 4 (= 63%).

Hence we recommend regression 4 model to Haulton

Requirement 2:

Considering the 'goodness-of-fit' measure and the 'significance of variables', for regression 4 and regression 5, it is observed that including an additional variable 'Merchandise Purchase (MP$)' has not increased the proportion of explained variation in the dependent variable 'Purchasing Department Costs (PDC)' and also considering the correlation coefficient between PDC and MP$, there is a weak positive correlation between the variables.

Hence we recommend regression 4 model to Haulton because with only 2 explanatory variables this model has been as good as regression 5