Chapter 11 formulas

Chapter 11 formulas - Lecture Notes Chapter Eleven: Simple...

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Lecture Notes Chapter Eleven: Simple Linear Regression Randall Miller 1 | Page Key Symbols o y Dependent variable (variable to be predicted) o x Independent variable (variable use to predict) o ( ) Ey Expected (mean) of y o 0 β y -intercept of true line o 1 Slope of true line o 0 ˆ Least squares estimate of y -intercept o 1 ˆ Least squares estimate of slope o ε Random error o ˆ y Predicted value of y for a given x -value o ( ) ˆ yy −→ Estimated error of prediction o SSE Sum of squared errors of prediction o r Coefficient of correlation o 2 r Coefficient of determination o p x Value of x used to predict y Formulas A First-Order (Straight-Line) Probabilistic Model 01 yx ββ = ++ Definition 11.1 The least squares line ˆˆ ˆ = + is the line that has the following two properties: 1. The sum of the errors (SE) equals zero. 2. The sum of squared errors (SSE) is smaller than that for any other straight-line model.
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Chapter 11 formulas - Lecture Notes Chapter Eleven: Simple...

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