# 10_09_1 - STAT 420 Examples for 10/09/2007 (1) Sales, y 5.0...

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STAT 420 Examples for 10/09/2007 (1) Fall 2007 Sales, y Advert, x 5.0 1.0 6.0 1.8 6.5 1.6 7.0 1.7 7.5 2.0 8.0 2.0 10.0 2.3 10.8 2.8 12.0 3.5 13.0 3.3 15.5 4.8 15.0 5.0 16.0 7.0 17.0 8.1 18.0 8.0 18.0 10.0 18.5 8.0 21.0 12.7 20.0 12.0 22.0 15.0 Polynomial Regression: Y i = β 0 + β 1 x i + β 2 x i 2 + … + β p – 1 x i p – 1 + e i , i = 1, 2, … , n , where e i ’s are independent Normal ( 0 , σ 2 ) . 1. It is well known that the sales response to advertising usually follows a curve reflecting the diminishing returns to advertising expenditure. As a company increases its advertising expenditure, sales increase, but the rate of increase drops continually after a certain point. If we consider company sales profits as a function of advertising expenditure, we find that the response function can be very well approximated by a second-order (quadratic) model. For a particular company, the data on monthly sales y and monthly advertising expenditure x , both in hundred thousand dollars, are given in the table on the right. Y i = β 0 + β 1 x i + β 2 x i 2 + e i n = 21. 23.0 14.4 > sales.dat <- read.table("http://www.stat.uiuc.edu/~stepanov/sales.dat", header = T) > par(pty="s") > plot(sales.dat\$Advert,sales.dat\$Sales)

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