Lecture25

Lecture25 - STAT 350 Lecture 25 Chapter 11 Inferential...

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STAT 350 Lecture 25 Chapter 11 Inferential Methods in Regression and Correlation
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linear regression Simple Linear Regression: Fit a line in the data when you see a linear trend Minimizing the errors using LS method Get estimates of slope and intercept accordingly
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Alternate calculations Meaning of slope b: How much does Y change if X is changed by 1 unit ? ( Rise over run ) Directly related to the correlation x y s s r b
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S xy ( x i x )( y i y ) x i y i 1 n ( x i )( y i ) S xx ( x i x ) 2 x i 2 1 n ( x i ) 2 S yy ( y i y ) 2 y i 2 1 n ( y i ) 2 Some Useful Formulas (page 108)
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Example 3.7 on page 117 Find the equation for the regression line. Summary statistics are given: n 20 x i 2817.9 y i 1574.8 x i 2 415,949.85 x i y i 222,657.88 y i 2 124,039.58
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Example 3.7 on page 117 Step 1 -- Find the slope b: n 20 x i 2817.9 y i 1574.8 x i 2 415,949.85 x i y i 222,657.88 y i 2 124,039.58 b S xy S xx x i y i 1 n ( x i )( y i ) x i 2 1 n ( x i ) 2 222,657.88 1 20 (2817.9)(1574.8) 415,949.85 1 20 (2817.9) 2 776.434 18,921.83 0.041
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Example 3.7 on page 117 Step 2 -- Find the intercept a: n 20 x i 2817.9 y i 1574.8 x i 2 415,949.85 x i y i 222,657.88 y i 2 124,039.58 b 0.041 a y bx 1574.8 20 0.041* 2817.9 20 78.74 0.041*140.895 72.96 The equation for the regression line is ˆ y 72.96 0.041 x
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Lecture25 - STAT 350 Lecture 25 Chapter 11 Inferential...

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