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PPT7 Variable Screening Techniques0

# PPT7 Variable Screening Techniques0 - McGill University...

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Variable Screening Methods Stepwise Regression All-Possible-Regressions (Best subsets)
Stepwise Regression Variables are entered into the model in order of significance (based on -values or F-values) until the new value being added is not significant. If introducing a new variable causes an existing variable to become non-significant it is dropped from the model.

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Data Y X 1 X 2 X 3 X 4 STORE PROFIT ADVERT SPECIAL SIZE PLACE 1 9.4 3 1 30 1 2 10.3 3 5 37 1 3 10.9 4 5 38 1 4 9.9 4 2 35 1 5 12.9 5 6 40 0 6 11.8 5 6 40 0 7 11.5 6 2 39 1 8 13.2 6 5 45 0 9 12.8 7 5 41 0 10 12.1 7 1 41 0
Correlation Matrix Profit Advert Special Size Place Profit 1 Advert .8056 1 Special .5037 0 1 Size .9145 .7577 .5014 1 Place -.8604 -.7071 -.4126 -.7318 1 First Second

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Minitab’s Stepwise Regression
Minitab’s Methods Screen

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Minitab: Stepwise Regession output
Minitab’s Stepwise Regression Results Minitab selected Model 6 0 3 3 4 4 3 4 ˆ 4.231 .201 1.033 y x x Y x x β β β ε = + + + = + - This model explains Profit ( Y ) in terms of variables Size ( x 3 ) and Place ( x 4 )

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Forcing a variable into the model Suppose that the manager in charge of advertising budgets insists that she needs a model that contains the variable advert ( x 1 ). In the next slide we show how to force the variable advert into the model.
Forcing a variable into the model

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Stepwise Regression with Advert in Model
Stepwise Regression with X 1 = advert forced into the model Stepwise regression has selected Model 2 0 1 1 2 2 1 2 ˆ 6.666 .715 .326 y x x Y x x β β β ε = + + + = + + Advert ( x 1 ) and Special ( x 2 ) are the selected variables

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Summary We see that Stepwise regression can help the analyst find a suitable model with important variables included as required for a specific application. Once we have decided upon the independent variables to include in a model it is important to check for possible interaction among the variables.