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Unformatted text preview: STAT 420 Examples for 09/11/2007 Fall 2007 The (normal) simple linear regression model: y i = + 1 x i + i , where i s are independent Normal ( , 2 ) ( iid Normal ( , 2 ) ). , 1 , and 2 are unknown model parameters. Suppose x i s are fixed (not random). & Y i s are independent Normal ( + 1 x i , 2 ) random variables. 1 & = ( ) ( ) -- 2 Y x x x x i i i ~ N ( ) - 2 2 1 & , x x i & = x & Y 1- ~ N ( ) - 2 2 2 & , x x n x i i = N ( ) - + 1 , 2 2 2 & x x x n i ( ) 2 1 2 & & Y 2 1 S i i e x n --- = ( ) 2 2 S 2 e n- ~ 2 ( n 2 ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Confidence interval for 1 : ( ) - 2 2 1 t & e x x s i SXX e s 2 1 t & where 2 t is the appropriate value of t-distribution with n 2 degrees of freedom. Test statistic for H : 1 = 10 : T = ( ) SXX i e e s x x s 10 1 2 10 1 & & & & - =-- ( n 2 degrees of freedom ) 1. The owner of Momma Leonas 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 Leonas 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:...
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- Spring '07
- Linear Regression