Describe  the  economic  meaning  and  statistical  significance  of  each  individual independent variable included in the Mrs. Smyth’s frozen fruit pie demand equation.  B.  Interpret the coefficient of determination (R2) for the Mrs.  Smyth’s frozen fruit pie demand equation.  C.  Use  the  regression  model  and  2007-4  data  to  estimate  2008-1  unit  sales  in  the Washington-Arlington-Alexandria market.  D.  To illustrate use of the standard error of the estimate statistic, derive the 95 percent  and  99  percent    confidence  intervals  for  2008-1  unit  sales  in  the  Washington-Arlington-Alexandria market

  • Demand Estimation for Mrs. Smyth’s Pies  Demand  estimation  for  brand-name  consumer  products  is  made  difficult  by  the  fact  that managers must rely on proprietary data.  There simply is not any publicly available data which can be used to estimate demand elasticities for brand-name orange juice, frozen entrees, pies, and the  like–and with good reason.   Competitors  would be  delighted to know  profit margins across  a  broad  array  of  competing  products  so  that  advertising,  pricing  policy,  and  product development strategy could all be targeted for maximum benefit.  Product demand information is valuable and jealously guarded. To see the process that might be undertaken to develop a better understanding of product demand  conditions, consider  the  hypothetical  example  of  Mrs.  Smyth’s Inc.,  a  Chicago-based food company.  In early 2008, Mrs. Smyth’s initiated an empirical estimation of demand for its gourmet frozen fruit pies.  The firm is formulating pricing and promotional plans for the coming year, and management is interested in learning  how pricing and promotional decisions might affect sales.  Mrs. Smyth’s has been marketing frozen fruit pies for several years, and its market research department  has collected  quarterly data  over two  years for  six important  marketing areas,  including  sales  quantity,  the  retail  price  charged  for  the  pies,  local  advertising  and promotional expenditures,  and  the price charged by a  major competing  brand  of frozen pies. Statistical data published by the U.S. Census Bureau (http://www.census.gov) on population and disposable  income  in  each  of  the  six  Metropolitan  Statistical  Areas  were  also  available  for analysis.  It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand.  These data appear in Table 5.3.  The following regression equation was fit to these data:    Qit = b0 + b1Pit + b2Ait + b3PXit + b4Yit + b5Popit + b6Tit + uit  Q  is  the quantity  of  pies  sold  during  the tth  quarter;  P  is  the retail  price  in  dollars  of  Mrs. Smyth’s frozen pies; A represents the dollars spent for advertising; PX is the price, measured in dollars, charged for  competing premium-quality  frozen fruit pies; Y  is  the median   dollars of disposable income per household; Pop is the population of the market area; T is the trend factor (2006-1 = 1, .  . . , 2007-4  =  8); and  uit is a  residual  (or disturbance) term.   The subscript i indicates  the regional  market  from  which  the  observation  was  taken,  whereas  the subscript  t represents the quarter during which the observation occurred.  Least squares estimation of the regression equation on the basis of the 48 data observations (eight quarters of data for each of six areas) resulted in the estimated regression coefficients and other statistics given in Table 5.4.
  • A.  Describe  the  economic  meaning  and  statistical  significance  of  each  individual independent variable included in the Mrs. Smyth’s frozen fruit pie demand equation.  B.  Interpret the coefficient of determination (R2) for the Mrs.  Smyth’s frozen fruit pie demand equation.  C.  Use  the  regression  model  and  2007-4  data  to  estimate  2008-1  unit  sales  in  the Washington-Arlington-Alexandria market.  D.  To illustrate use of the standard error of the estimate statistic, derive the 95 percent  and  99  percent    confidence  intervals  for  2008-1  unit  sales  in  the  Washington-Arlington-Alexandria market.  TABLE 5.4 Estimated Demand Function for Mrs. Smyth’s Gourmet Frozen Fruit Pies       Variable Coefficient Standard Error of Coefficient t statistic   (1) (2) (3) (4) = (2)/(3)   Intercept 529,774 271,331 1.95   Price (P) -122,607 16,422 -7.47   Advertising (A) 5.838 1.65 3.54   Competitor Price (PX) 29,867 13,449 2.22   Income (Y) 2.043 3.762 0.54   Population (Pop) 0.030 0.004 7.50   Time (T) 2,815 4,539 0.62         Coefficient of Determination = R2 = 87.1%    Corrected Coefficient of Determination = R2 = 85.2%    F statistic = 45.16      Standard Error of the Estimate = SEE = 67,584

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