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 . The quarterly data on average variable cost (AVC), 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: Q = d + eP + fM + gP , dH 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/Year Period (t) AVC Q P M PH 1st/2006 1 109 1647 275 58000 175 2nd/2006 2 118 1664 275 58000 175 3rd/2006 3 121 1295 300 58000 200 4th/2006 4 102 1331 300 56300 200 1st/2007 5 121 1413 300 56300 200 2nd/2007 6 102 1378 300 56300 200 3rd/2007 7 105 1371 300 57850 200 4th/2007 8 101 1312 300 57850 200 1st/2008 9 108 1301 325 57850 250 2nd/2008 10 113 854 350 57600 250 3rd/2008 11 114 963 350 57600 250 4th/2008 12 105 1238 325 57600 225 1st/2009 13 107 1076 325 58250 225 2nd/2009 14 104 1092 325 58250 225 3rd/2009 15 104 1222 325 58250 225 4th/2009 16 102 1308 325 58985 250 1st/2010 17 116 1259 325 58985 250 2nd/2010 18 126 711 375 58985 250 3rd/2010 19 116 1118 350 59600 250 4th/2010 20 139 91 475 59600 375 1st/2011 21 152 137 475 59600 375 2nd/2011 22 116 857 375 60800 250 3rd/2011 23 127 1003 350 60800 250 4th/2011 24 123 1328 320 60800 220 1st/2012 25 104 1376 320 62350 220 2nd/2012 26 114 1219 320 62350 220 3. Apply dummy variables to construct the time-series quarterly sales estimation of Sting Ray (Hint: Q = A+Bt+D1t...). Please predict the quantity sold in the first quarter 2014. 4. Run the log-linear regression to estimate the demand function for Sting Rays. Evaluate the statistical significance of the three estimated coefficients of parameters by using a significance level of 5 percent. Discuss the elasticities (price elasticity of demand, income elasticity and cross-price elasticity) to define the characters of Sting Ray.