Question

The following is information pertaining to a local fitness club, Fitness for Life.
Month	Club Membership (number of members)	Total Operating Costs
July	450	$                      8,900
August	480	$                      9,800
September	500	$                   10,100
October	550	$                   10,150
November	560	$                   10,500
December	525	$                   10,200
1. By looking at the Total Operating Costs and the Average Operating Costs Per Member, can you tell whether the club's operating costs are variable, fixed, or mixed?
2. Perform Regression analysis using Microsoft Excel. What is the monthly operating cost equation? What is the R-square?
3. Use the high-low method to determine the club's monthly operating cost equation.
4. Can we predict total montly operating costs if the club has 3,000 members?

Answer 1

1.
The cost is mixed cost, since cost is increasing with increase in output but not with direct proportion

2. Cost equation = $3912.35 + $11.80 x
R Square = 0.8007

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.894816
R Square	0.800696
Adjusted R Square	0.75087
Standard Error	278.0903
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1242747	1242747	16.06982	0.016014
Residual	4	309336.8	77334.19
Total	5	1552083
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3912.354	1508.329	2.593834	0.060439	-275.438	8100.146	-275.438	8100.146
Number of Members	11.8029	2.944307	4.008718	0.016014	3.62819	19.9776	3.62819	19.9776

3. High low method
Variable cost per unit = ($10500-8900)/(560-450) = $14.55 per unit
Fixed Cost = 10500 - 560 x 14.55 = $2352

Cost Equation = $2352 + 14.55 x

4. Cost for 3000 members
using high low equation = $2352 + 14.55 x 3000 = $46002
using regression = $3912.35 + 11.80 x 3000 = $39312.35

If you have any query regarding this, kindly comment with your query