Multiple Regression Analysis for a Special Decision Requires

Multiple Regression Analysis for a Special Decision (Requires Computer Spreadsheet)
For billing purposes, South Town Health Clinic classifies its services into one of four major procedures,
X1 through X4. A local business has proposed that South Town provide health services to its
employees and their families at the following set rates per procedure:
X1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 45
X2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
X3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
X4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Because these rates are significantly below the current rates charged for these services, management
has asked for detailed cost information on each procedure. The following information is
available for the most recent 12 months.
Number of Procedures
Mont Total cost X1 X2 X3 X4
1 . . . . . . . . . . . . . $23,000 30 100 205 75
2 . . . . . . . . . . . . . 25,000 38 120 180 90
3 . . . . . . . . . . . . . 27,000 50 80 140 150
4 . . . . . . . . . . . . . 19,000 20 90 120 100
5 . . . . . . . . . . . . . 20,000 67 50 160 80
6 . . . . . . . . . . . . . 27,000 90 75 210 105
7 . . . . . . . . . . . . . 25,500 20 110 190 110
8 . . . . . . . . . . . . . 21,500 15 120 175 80
9 . . . . . . . . . . . . . 26,000 60 85 125 140
10 . . . . . . . . . . . . 22,000 20 90 100 140
11 . . . . . . . . . . . . . 22,800 20 70 150 130
12 . . . . . . . . . . . . . 26,500 72 60 200 120
Required
a. Use multiple regression analysis to determine the unit cost of each procedure. How much
variation in monthly cost is explained by your cost-estimating equation?
b. Evaluate the rates proposed by the local business. Assuming South Town has excess capacity
and no employees of the local business currently patronize the clinic, what are your recommendations
regarding the proposal?
c. Evaluate the rates proposed by the local business. Assuming South Town is operating at capacity
and would have to turn current customers away if it agrees to provide health services to the
local business, what are your recommendations regarding the proposal?

For a, I ran regression and got the each unit cost fo each procedure but i don\'t know how to analysis the questions a, b, c. Thanks.

101.0161074

Solution

a.

The regression equation is

Y = -3967.58 + 56.78X₁+ 64.27X₂ + 52.99X₃ + 101.02X₄

This is a strong regression equation. 97.78% of the variation in monthly cost is explained by your cost-estimating equation.

b.

The desirability of the proposal depends on the mix of services used by the employees of the local business. If the mix contained a significant portion of X1, the proposal might not be desirable.

c.

According to the given information, the proposed rates are significantly below the current rates. Hence, accepting the proposal would require turning away regular customers who pay more for the identical services.