PoolVac, Inc. manufactures and sells a single product called the "Sting Ray," which is a patent-protected automatic cleaning device for swimming pools. PoolVac's Sting Ray faces its closest competitor, Howard Industries, also selling a competing pool cleaner. Using the last 26 quarters of production and cost data, PoolVac wishes to estimate its average variable costs using the following quadratic specification :

AVC = a + bQ + cQ2, (0.1)

The quarterly data on average

variable cost (AV C), and the quantity of Sting Rays produced and sold each

quarter (Q) are presented in the data file. PoolVac also wishes to use its

sales data for the last 26 quarters to estimate demand for its Sting Ray.

Demand for Sting Rays is specified to be a linear function as the following :

Qd =d+eP+fM+gPH, (0.2) in which its

price (P), average income for households in the U.S. that have swimming pools

(M), and the price of

the competing pool cleaner sold by

Howard Industries (PH).

Sting Ray-PoolVac, Inc.

Quarter/YearPeriod (t)AVCQPMPH

1st/20061 109214723258000132

2nd/20062 118216423258000132

3rd/20063 121179531358000213

4th/20064 102183131356300213

1st/20075 121191331356300213

2nd/20076 102187831356300213

3rd/20077 105187131357850213

4th/20078 101181231357850213

1st/20089 108180132657850250

2nd/200810 113135436057600260

3rd/200811 114146336057600260

4th/200812 105173832657600226

1st/200913 107157632658250226

2nd/200914 104159232658250226

3rd/200915 104172232658250226

4th/200916 102180832658985260

1st/201017 116175932658985260

2nd/201018 126121137358985260

3rd/201019 116161836059600260

4th/201020 13959148259600382

1st/201121 15263748259600382

2nd/201122 116135737360800260

3rd/201123 127150336060800260

4th/201124 123182833060800230

1st/201225 104187633062350230

2nd/201226 114171933062350230

1. Run the appropriate regression to estimate the average variable cost function (AV C) (equation 0.1) for Sting Rays. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent. Be sure to comment on the algebraic signs of the three parameter estimates. (20%)