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10_18 - STAT 420 Examples for Spring 2007 1 The marketing...

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STAT 420 Examples for 10/18/2007 Spring 2007 1. The marketing manager of a large supermarket chain would like to determine the effect of shelf space and whether the product was placed at the front or back of the aisle on the sales of pet food. A random sample of 12 equal-sized stores is selected with the following results: Store Shelf Space (feet) Location Weekly Sales (hundreds of dollars) 1 5 Back 1.6 2 5 Front 2.2 3 5 Back 1.4 4 10 Back 1.9 5 10 Back 2.4 6 10 Front 2.6 7 15 Back 2.3 8 15 Back 2.7 9 15 Front 2.8 10 20 Back 2.6 11 20 Back 2.9 12 20 Front 3.1 Consider the model Y = β 0 + β 1 x 1 + β 2 x 2 + e , where the dummy variable x 2 is the indicator for the front of the aisle ( i.e., x 2 = 1 for front, x 2 = 0 for back ). For the back of the aisle: Y = β 0 + β 1 x 1 + e . For the front of the aisle: Y = β 0 + β 1 x 1 + β 2 + e = ( β 0 + β 2 ) + β 1 x 1 + e . The dummy variable splits the regression relationship into two parallel lines, one for each level ( 0 or 1 ) of the qualitative dummy variable. The distance between the two parallel lines ( measured as the distance between the two y-intercepts ) is equal to the estimated coefficient of the dummy variable x 2 .

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> x1 <- c( 5, 5, 5, 10, 10, 10, 15, 15, 15, 20, 20, 20) > x2 <- c( 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1) > y <- c(1.6,2.2,1.4,1.9,2.4,2.6,2.3,2.7,2.8,2.6,2.9,3.1) > petfood <- lm(y ~ x1 + x2) > summary(petfood) Call: lm(formula = y ~ x1 + x2) Residuals: Min 1Q Median 3Q Max -0.2700 -0.1325 -0.0650 0.1125 0.3600
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10_18 - STAT 420 Examples for Spring 2007 1 The marketing...

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