A furniture company has opened a small plant that builds tables. Jill, the production manager, knows the fixed cost of the plant, F = $78 per day, and includes the cost of the building, tools, and equipment. Variable costs include labor, energy costs, and wood. Jill wants to know the cost function. She conducts an experiment in which she varies the daily production level over a 10-day period and observes the associated daily cost. The daily output levels assigned are 1, 2, 4, 5, 7, 8, 10, 12, 15, and 16. The associated total costs for these output levels are 125, 161, 181, 202, 207, 222, 230, 275, 390, and 535, respectively. 

a. Use the Trendline tool in Excel to estimate a cost function by regressing cost on output.Try a linear specification (C=a+bq), a quadratic specification (C = a + bq + dq²), and a cubic specification (C = a + bq + dq² + eq³). Based on the plotted regressions, which specification would you recommend that Jill use? Would it make sense to use the Set Intercept option? If so, what value would you choose?

b. Generate the corresponding average cost data by dividing the known cost by output for each experimental output level. Estimate an average cost curve using the Trendline tool.