Question

The owner ot Showtime Movie Theaters, Inc., would ike to prodict wecey grosa revenue as a function of advertising expenditures. Historical data for a sample of cight weeks tollow. Weekly Television Newspaper Advertising Advertising ($1,000s)(1,000s) (1,000s) 5.0 2.0 96 1.5 2.0 1.5 90 3.5 2.5 3.0 94 (a) Develop an etimated regression equation with the amount of television adwartising as the indapendent variable. (Round your numerical values to two decimal places. Lot x represent the amount of television advertising in $1,000s and y represent the woakiy gross revenue in $1,000s. b Develop an "tima ed egress on equation with both tale ision advertising and rewspaper advertising as the independent variables advertising in $1,000s, and y represent the weekly gross revenue in $1,000s Round your n marica values to two deam 1 paces. Lat x1 represent the amount of te evsion adva in孚1 000s, x2 apresent the amount of news aper si (c) Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? -Select-9.is in part (a) andin part( Interpret the coefficient in each case n part a it rep esents the change in revenue due to a one-unk increase in television ad¥ertising expenditure with ne spaper advertisi g held constant. In part b it re resents the chang. in revenue due to a one unit increase in newspaper advertising with television advertising held n part a it represents e c ange in revenue due to a one-unit ncrease in newspaper a vertising expen ture with teevtsion advertsng he constant n part b it represents the change in evenue due to ฎิ one-unit increase in television advertising with newspaper advertising held n part a it represents t e change in revenue due to a 0na-unt increaGe in television advertising with newspaper advertising held constant. In part it represents thฉ Chan e n revenue due to a one-unit increase in ek ision ad ertain expenditure @ D 0 0 In part (a) it represents the change in revenue due to a one-unik increase in television advertising expenditure. In pert (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant n part a it represents the change in revenu due to a one-unk increase in television advertising expenditure. In part b re resents the change in revenue due to a one-unit increase in ne spaper advertisng with television advertising held constant. d) predict weekly gross evenue in dollars for a西eek when 3,900 is spent on television advertising and 1,400 is spent on newspaper advertising. Round your ans er to the nearest cent

Answer 1

XValues YValues 96 90 95 92 95 94 94 94 100 2.5 98 3.5 2.5 5 96 M: 3.1875 M: 93.75 94 92 90s x-Independent Regression Line -1.6X 88.64) Estimate Calculation Summary Sum of X 25.5 sum of Y 750 Mean X3.1875 Mean Y 93.75 Sum of squares (SSx 6.4688 Sum of products (SP) 10.375 Regression Equation -y-bX+ a b- SP/SSx- 10.38/6.47 1.60386 a My - bMx 93.75 (1.6 3.19)- 88.63768 у-1.60386x+ 88.63768 X- Mx Y- M (X- Mx)2 (X- Mx)(Y- My 1.8125 1.1875 0.8125 0.6875 0.1875 0.3125 0.6875 0.1875 2.25 3.75 1.25 1.75 1.25 0.25 0.25 0.25 3.2852 1.4102 0.6602 0.4727 0.0352 0.0977 0.4727 0.0352 4.0781 4.4531 1.0156 1.2031 0.2344 0.0781 -0.1719 0.0469 SS: 6.4688 SP: 10.375

X1 Values X2 Values YValues 4 94 94 94 M: 3.1875 M: 2.475 M: 93.75 Predictor X1Predictor X2 Calculation Summary Sum of X1 25.5 Sum of X2 19.8 Sum of Y-750 Mean X1 3.1875 Mean X2= 2.475 Mean γ= 93.75 Sum of squares (SSx 6.4688 Sum of squares (SSx2) 5.815 Sum of products (SP1) 10.375 Sum of products (SPx2)-0.25 Sum of products (SPxix2)-3.4125 Regression Equation-y bjX1+ b2X2+ a (SSx2)-(SPxix2) (SP1x2)- 59.48/25.97-2.29018 (SSx2)-(SPxix2) (SPx1x2) 33.79/25.97- 1.30099 a My byMx1-b2Mx2 93.75-(2.29*3.19)- (1.3*2.48)-83.23009 2.29018X11.30099X2 83.23009 X1-Mx1 X2-Mx2 1.813 1.188 0.813 0.688 0.188 0.313 -0.688 -0.188 0.975 -0.475 -0.975 0.025 0.825 0.175 1.725 0.025 4.078 4.453 1.016 1.203 0.234 0.078 0.172 0.047 -2.194 1.781 -1.219 -0.044 1.031 0.044 0.431 0.006 -1.767 0.564 0.792 -0.017 -0.155 0.055 1.186 0.005 3.285 0.951 0.226 0.951 0.001 0.681 0.031 2.976 0.001 -3.75 0.66 0.473 0.035 0.098 0.473 0.035 0.25 0.25 0.25 SSX1 SSX2 SPX1Y SPX2Y SPX1X2 6.469 5.815 10.375 -3.413

ヘ 1. 604 x, & g 64 y 2.29

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