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Lect25_L6_L7_handout

Lect25_L6_L7_handout - lecture 25 Linear Regression III...

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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
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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 0 if H 0 : β 1 = 0 H a : β 1 = 0 | t | > t α/ 2 , or, equivalently p (= Area under t outside of [ -| t | , | t | ] ) < α H 0 : β 1 0 H a : β 1 > 0 t > t α , or, equivalently p (= Area under t to right of t ) < α H 0 : β 1 0 H a : β 1 < 0 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 ( 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 / SS xx ,
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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 0 - ¯ x ) 2 SS xx , and t α/ 2 is based on n - 2 degrees of freedom.
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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
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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
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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
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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
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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 Using Information in X
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