Multiple Regression

In the McCourt Company example, fill in the blank percent of the variability in materials handling cost was explained by changes in the number of moves. As a result, McCourt may want to search for additional explanatory variables. For example, the weight of the items moved might be usefulparticularly if forklifts and other heavy machinery are needed for moving parts and products from one location to another.

In the case of two explanatory variables, the linear equation is expanded to include the additional variable:

Y = F + V₁X₁ + V₂X₂

where

X₁ = Number of moves

X₂ = Number of pounds moved

With three variables (Y, X₁, X₂), a minimum of three points is needed to compute the parameters F, V₁, and V₂. Seeing the points becomes difficult because they must be plotted in three dimensions. Using the scatterplot method or the high-low method is not practical.

However, the extension of the method of least squares is straightforward. It is relatively simple to develop a set of equations that provides values for F, V₁, and V₂ that yields the best-fitting equation. Whenever least squares is used to fit an equation involving two or more independent variables, the method is called multiple regression. The computations required for multiple regressions are far more complex than in simple (one independent variable) regression and any practical application of multiple regression requires use of regression software. The reliability measures are basically the same for multiple regressions as they were for a regression involving a single variable.

Applying the Concepts

The staff of controller of McCourt Company added the variable "pounds moved" to the ten-month data set:

Month	Materials Handling Cost	Number of Moves	Pounds Moved
January	$5,600	475	12,000
February	3,090	125	15,000
March	2,780	175	7,800
April	8,000	600	29,000
May	1,990	200	600
June	5,300	300	23,000
July	4,300	250	17,000
August	6,300	400	25,000
September	2,000	100	6,000
October	6,240	425	22,400

Required:

1. Using the data on material handling, use regression software such as Microsoft Excel to complete the missing data in the table below (round regression parameters to the nearest cent and other answers to three decimal places):

McCourt Company SUMMARY OUTPUT
Regression Statistics
Multiple R	0.999
R Square	fill in the blank
Adjusted R Square	fill in the blank
Standard Error	119.600
Observations	10

ANOVA
	df	SS	MS	F	Significance F
Regression	2	37,768,070.16	18,884,035	1,320.168	9.50629E-10
Residual	7	100,129.84	14,304.26
Total	9	37,868,200.00

	Coefficients	Standard Error	t Stat	P-value
Intercept	fill in the blank	86.068	6.863	0.000239
X Variable 1	fill in the blank	0.340	0.340	9.81E-08
X Variable 2	fill in the blank	0.006	17.446	5E-07

2. Using the cost equation from Requirement 1, calculate the total expected material handling cost for November if 350 moves are expected and 17,000 pounds of material will be moved (round final answer to the nearest dollar).

Expected material handling cost: $ fill in the blank

3. For the coming year, McCourt expects 3,940 moves involving a total of 204,000 pounds. Calculate the following:

Total expected fixed costs (round to the nearest dollar): $ fill in the blank Total material handling cost (add each component in the equation and then round to the nearest dollar): $ fill in the blank