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Stat Final

In: Other Topics

Submitted By bodwell1129
Words 2068
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Modeling Qualitative Variable (Dummy Variables) with Regression
Modeling values as base and differences
Base price: $299.99
MS office and Student 2010: $299.99+$119=$418.99
MS office home and business 2010: $299.99+$199=$498.99
MS office Pro 2010: $299.99+$349=$648.99
Since we must use 1 and 0 to represent yes and no, we can model…Price=299.99+119(X1)+199(X2)+349(X3)
If you choose X1: put 1 in the X1 and others 0, If you choose X2: put 1 in the X2 and others 0….
NOTE: Intercept will be the base price.
Ex) model the following computers
Computer1, base computer with 1 year support $338.99
Computer2, 90 day support $299.99 Answer) 338.99-39(X1)+80(X2)
Computer3, 2 year support $418.99
Using averages: if you are purchasing the same type of computer across many dealers, some prices will be higher and some will be lower, therefore we average the prices.
Average price = 300+50(option1)+200(option2)-140(option3). Here we have 4 option: base, option1, option2, option3
If there are 5 options, 4 dummy variables would be needed, base, option1, option2, option3, option4.
In general, we will model a qualitative variable with “c” levels using “c-1” dummy variables.
Population Mean of Y = 0 + 1X1 + 2X2 + … + + c-1Xc-1
What would be the base average price? 0 = μc
What would represent? 0 + 1X1 + 2X2 +X3 => if you choose level 3, 0+μ3 =>  μ3- μc
What would be the population mean of level 2? 0+μ2 => μ2- μc
Error due to sampling: if you are able to obtain only a sample of prices, the averages and the changes in average price due to changing options would be in error (Second building block: all estimates are wrong)
Example: You are measuring the tensile strength provided by 4 suppliers. Supplier 1 has been your supplier in the past and will be considered your base level. You create 3 dummy variables: X1 = 1 if

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