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# 08_30 - STAT 420 Examples for Fall 2007 The(normal simple...

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STAT 420 Examples for 08/30/2007 Fall 2007 The (normal) simple linear regression model: y i = β 0 + β 1 x i + ε i , where ε i ’s are independent Normal ( 0 , σ 2 ) ( iid Normal ( 0 , σ 2 ) ). β 0 , β 1 , and σ 2 are unknown model parameters. Least-Squares Approach: minimize ( ) ( ) = + - n i i i x y 1 2 1 0 ( ) ( ) & - = - = n x x x x i i i SXX 2 2 2 ( ) ( ) ( ) ( ) ( ) & - = - = - - = n y x y x y x x y y x x i i i i i i i i SXY ( ) ( ) & - = - = n y y y y i i i SYY 2 2 2 Slope 1 ˆ = SXX SXY Y-intercept 0 ˆ = x y ˆ 1 -

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1. The owner of Momma Leona’s Pizza restaurant chain believes that if a restaurant is located near a college campus, then there is a linear relationship between sales and the size of the student population. Suppose data were collected from a sample of 10 Momma Leona’s Pizza restaurants located near college campuses. For the i th restaurant in the sample, x i is the size of the student population (in thousands) and y i is the quarterly sales (in thousands of dollars). The values of x i and y i for the 10 restaurants in the sample are summarized in the following table: Restaurant Student Population (1000s) Quarterly Sales (\$1000s) i x i y i 1 2 58 2 6 105 3 8 88 4 8 118 5 12 117 6 16 137 7 20 157 8 20 169 9 22 149 10 26 202 0 50 100 150 200 250 0 5 10 15 20 25 30
a) Find the equation of the least-squares regression line. x

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08_30 - STAT 420 Examples for Fall 2007 The(normal simple...

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