Chapter 10, Problem 10.31E

Regression analysis, service company. (CMA, adapted) Linda Olson owns a professional character business in a large metropolitan area. She hires local college students to play these characters at children’s parties and other events. Linda provides balloons, cupcakes, and punch. For a standard party the cost on a per-person basis is as follows:

Balloons, cupcakes, and punch	$ 7
Labor (0.25 hour × $20 per hour)	5
Overhead (0.25 hour × $40 per hour)	10
Total cost per person	$22

Linda is quite certain about the estimates of the materials and labor costs, but is not as comfortable with the overhead estimate. The overhead estimate was based on the actual data for the past 9 months, which are presented here. These data indicate that overhead costs vary with the direct labor-hours used. The $40 estimate was determined by dividing total overhead costs for the 9 months by total labor-hours.

Month	Labor-Hours	Overhead Costs
April	1,400	$ 65,000
May	1,800	71,000
June	2,100	73,000
July	2,200	76,000
August	1,650	67,000
September	1,725	68,000
October	1,500	66,500
November	1,200	60,000
December	1,900	72,500
Total	15,475	$619,000

Linda has recently become aware of regression analysis. She estimated the following regression equation with overhead costs as the dependent variable and labor-hours as the independent variable:

$y=\$43,563+\$14.66X$

1. 1. Plot the relationship between overhead costs and labor-hours. Draw the regression line and evaluate it using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

  Required

1. 2. Using data from the regression analysis, what is the variable cost per person for a standard party?
2. 3. Linda Olson has been asked to prepare a bid for a 20-child birthday party to be given next month. Determine the minimum bid price that Linda would be willing to submit to recoup variable costs.