# High-low method and regression

High-low method and regression analysis. Happy Business College has recently opened a restaurant as part of its hospitality major. For the first 10 weeks the manager did not estimate any costs, but instead hoped revenues would cover costs. One of the new waiters, who happens to be taking a cost accounting class, suggests that the manager take the past known weekly costs and try to determine a cost equation by relating the cost to the number of customers served. The cost and customer data are as follows:

The manager gives this information to the waiter, who runs a regression and gets the following equation:

Weekly total restaurant costs = \$2,453 + (\$19.04 × Number of customers per week)

1. Plot the relationship between number of customers per week and weekly total restaurant costs.

2. Estimate the cost equation using the high-low method, and draw this line on your graph.

3. Draw the regression line on your graph. Use your graph to evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Is the cost function estimated using the high-low method a close approximation to the cost function estimated using the regression method. Explain briefly.

4. At what point (number of customers) will the expected total cost based on the high-low equation equal the expected total cost based on the regression equation?

# High-low method and regression

High-low method and regression analysis Local Harvest, a cooperative of organic familyowned farms outside of Columbus, Ohio, 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 to the nearby suburban community. Families pay a seasonal membership fee of \$50, and place their orders a week in advance for a price of \$40 per week. In turn, Local Harvest delivers fresh-picked seasonal local produce to several neighborhood points. Eight hundred families joined the club for the first season, but the number of orders varied from week to week. Harvey Hendricks has run the produce club for the first 10-week season. Before becoming a farmer, Harvey had been a business major in college, and he remembers a few things about cost analysis. In planning for next year, he wants to know how many orders will be needed each week for the club to break even, but first he must estimate the club’s fixed and variable costs. He has collected the following data over the club’s first 10 weeks of operation:

Required

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. Harvey uses his computer to calculate the following regression formula:

Total weekly costs = \$8,631 + (\$31.92 x Number of weekly orders)

Draw the regression line on your graph. Use your graph to evaluate the regression line using the criteria of economic plausibility, goodness of fit, and 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.

4. Did Fresh Harvest break even this season? Remember that each of the families paid a seasonal membership fee of \$50.

5. Assume that 900 families join the club next year, and that prices and costs do not change. How many orders, on average, must Fresh Harvest receive each week to breakeven?