lecture_chp12_8 - Lecture Examples Topic 8 Models with...

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Lecture & Examples Topic 8: Models with Qualitative Independent Variable Model with One Qualitative Independent Variable with k Levels: Suppose we want to develop a model for the mean yield per acre, E ( y ), of four different varieties of snow peas (A, B, C, and D). Notice that we can not assign a quantitative measure for a given variety of snow pea. Although we can assign 1, 2, 3, and 4 to these four varieties of snow peas, these numbers have no meaningful quantitative interpretation. To solve this problem, we introduce the concept of a dummy variable. Let = = = variety other is pea snow the if 0 C variety is pea snow the if 1 variety other is pea snow the if 0 B variety is pea snow the if 1 variety other is pea snow the if 0 A variety is pea snow the if 1 3 2 1 x x x Then, we can write the following model equation: ε + β + β + β + β = 3 3 2 2 1 1 0 x x x y . 1
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Suppose that D C B A , , , μ μ μ μ is the mean yield for variety A, B, C, and D, respectively. Now, we can represent the mean yield of variety B by checking the dummy variable x 1 , x 2 , and x 3 . We can see that we should use x 1 = 0, x 2 = 1 and x 3 = 0 to get . ) 0 ( ) 1 ( ) 0 ( ) ( 2 0 3 2 1 0 B β + β = β + β + β + β = = μ y E Similarly, we can find that , 1 0 A β + β = μ , 3 0 C β + β = μ and . 0 D β = μ In general, we can write the model with one qualitative independent variable with k levels as follows: Step 1: Use k - 1 dummy variables.
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