30 Jan 3) significance of the independent varia
Case3: High-low method and regression analysis. Mars Co., a cooperative of organic family owned farms, has recently started a fresh produce club to provide support to the group’s member farms and to promote the benefits of eating organic, locally produced food. Families pay a seasonal membership fee of $100 and place their orders a week in advance for a price of $40 per order. In turn, Mars Co. delivers fresh-picked seasonal local produce to several neighborhood distribution points. Five hundred families joined the club for the first season, but the number of orders varied from week to week.
Pam Luck has run the produce club for the first season. Pam is now a farmer but remembers a few things about cost analysis from college. In planning for next year, she wants to know how many orders will be needed each week for the club to break even, but first she must estimate the club’s fixed and variable costs. She has collected the following data over the club’s first 12 weeks of operation:
Week Number of Orders per Week Weekly Total Costs
1 380 26,425
2 385 26,600
3 285 24,700
4 325 25,200
5 350 25,750
6 420 27,000
7 360 25,900
8 435 27,200
9 415 26,900
10 450 27,995
11 390 26,750
12 460 28,315
Required (1 thru 5 for written analysis):
1. Plot the relationship between number of orders per week and weekly total costs.
2. Estimate the cost equation using the high-low method, and draw this line on your graph.
3. Estimate the cost equation using the regression analysis, and provide the regression equation formula such as: Weekly total costs = A + ($B ? Number of orders per week)
4. Did Mars Co. break even this season? Remember that each of the families paid a seasonal membership fee of $100.
5. Assume that 500 families join the club next year and that prices and costs do not change. How many orders, on average, must Mars Co. receive each of 12 weeks next season to break even?
6 (For presentation only). Draw the regression line on your graph. Use your graph to evaluate the regression line using
1) the criteria of economic plausibility,
2) goodness of fit, and
3) significance of the independent variable.
Is the cost function estimated using the high-low method a close approximation of the cost function estimated using the regression method? Explain briefly.
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