Lect25_L6_L7_handout

Lect25_L6_L7_handout - lecture 25, Linear Regression III...

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Unformatted text preview: lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III Outline 1 The Simple Coefficient of Determination 2 The Simple Correlation Coefficient lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III Review The rules for testing the significance of the slope: Null Alternative Reject H if H : β 1 = H a : β 1 6 = | t | > t α/ 2 , or, equivalently p (= Area under t outside of [-| t | , | t | ] ) < α H : β 1 ≤ H a : β 1 > t > t α , or, equivalently p (= Area under t to right of t ) < α H : β 1 ≥ H a : β 1 < t <- t α , or, equivalently p (= Area under t to left of t ) < α where t = b 1 s b 1 = b 1 s / √ SS xx = b 1 p ( n- 2 ) SS xx √ SSE ! , and t α , t α/ 2 and p are based on t with df = n- 2 . A 100 ( 1- α )% confidence interval for the true slope β 1 is b 1 ± t α/ 2 s b 1 = b 1 ± t α/ 2 · s / p SS xx , lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III Review A 100 ( 1- α )% CI for the mean value of y is: ˆ y ± t α/ 2 s √ distance value , A 100 ( 1- α )% PI for an individual value of y is: ˆ y ± t α/ 2 s √ 1 + distance value , where Distance value = 1 n + ( x- ¯ x ) 2 SS xx , and t α/ 2 is based on n- 2 degrees of freedom. lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III Minitab Output of Regression, Fuel Consumption Data lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III Excel Output of Regression, Fuel Consumption Data lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III The Simple Coefficient of Determination The Simple Coefficient of Determination How useful is a particular regression model? One measure of usefulness is the simple coefficient of determination It is represented by the symbol r 2 lecture 25, Linear Regression III The Simple Coefficient of Determina- tion The Simple Correlation Coefficient lecture 25, Linear Regression III The Simple Coefficient of Determination Prediction Errors for Fuel Consumption Data When Not Using Information in X lecture 25, Linear Regression III The Simple Coefficient of...
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This note was uploaded on 12/30/2009 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

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Lect25_L6_L7_handout - lecture 25, Linear Regression III...

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