Is also called the fitted or predicted value ideally

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, is also called the fitted or predicted value. Ideally, our predicted values will be very close to our observed values. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 14 / 18
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Residuals Residuals are the difference between the observed and predicted values, i.e. ˆ e i = y i - ˆ y i The residuals measure how far much we missed by, and are going to be how we find formulas for our fitted equation. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 15 / 18
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Least Squares Regression We’ll say the best line to fit the data is the line that minimizes the sum of the squared residuals. (Did that sound like SSE to anyone?) Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 16 / 18
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Least Squares Formulas ˆ β = r s y s x ˆ α = ¯ y - ˆ β ¯ x Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 17 / 18
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Alternate formula for ˆ β ˆ β = SXY SXX where SXX = n X i =1 ( x i - ¯ x ) 2 = n X i =1 x 2 i - n ¯ x 2 SXY = n X i =1 ( x i - ¯ x )( y i - ¯ y ) = n X i =1 x i y i - n ¯ x ¯ y Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 18 / 18
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