ass3sol - Stat 231 Assignment 3 Solutions 1. In an...

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Stat 231 Assignment 3 Solutions 1. In an investigation to compare two new packaging strategies (here called A and B) for a consumer product, a marketing company selected 60 stores in one sales region. They randomly assigned strategy A to 30 stores and B to the remaining 30. The company then recorded the total sales ($) for the product over the next two-week period. For each store, they also determined the total sales of the same product (with the standard packaging) from the previous two weeks. The data can be accessed using the R code source(‘ 144725-_admin/_assoc/04C00F4D113D4ABE958960DCA3358257/Ass3q1source.txt’) The variates are labeled strategy, sales and past.sales. Consider the model: , ~ (0, ), , ; 1,. ..,30, independent ij i ij ij Y R R G i A B j μ σ = + = = to describe the repeated application of the Plan. Suppose the sales for the jth store with strategy i is y ij . a) Show that the least squares estimates of A and B are the average sales for each packaging strategy. We minimize W y y y A B ij i j i A B Aj A j Bj B j ( , ) ( ) ( ) ( ) , = - = - + - = = = = 2 1 30 2 1 30 2 1 30 with respect to A and B .The partial derivative of W with respect to A is = - - = W y A Aj A j 2 1 30 ( ). If we set this derivative to 0 and solve we get $ A A y = , the average of the response variate values for the stores receiving packaging strategy A. Similarly, we get the corresponding result for $ B . b) Write an expression for the estimated residual $ r r y ij ij i = - c) A histogram of the estimated residuals is on the following page. What does the plot tell us about the adequacy of the model? The histogram is not bell-shaped (it is skewed to the right) and hence there is some evidence that the gaussian modeling assumption for the ij R is incorrect.
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This note was uploaded on 11/21/2011 for the course MATH STAT 231 taught by Professor Marsh during the Spring '10 term at Waterloo.

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ass3sol - Stat 231 Assignment 3 Solutions 1. In an...

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