Chapter14ASW

# Chapter14ASW - .2 14.3 14.4 Simple Linear Regression Model...

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Chapter 14 §14.2, 14.3, 14.4 Simple Linear Regression Model True Regression Equation i i i x y ε β β + + = 1 0 Estimated Regression Equation x b b y 1 0 ˆ + = i x denotes the value of the independent variable for the i th observation, and i y denotes the value of the response variable for the i th observation. n denotes the number of observations. y ˆ is the predicted value of the response when the independent variable has the value x b 1 = ( 29 ( 29 ( 29 - - - 2 x x y y x x i i i = - - 2 2 x n x y x n y x i i i b 0 = x b y 1 - Five observations have yielded the results recorded in the table to the right. observation x y 1 4 2 2 5 4 3 5 6 4 8 12 5 8 16 a) Find the estimated regression equation. b) Find the predicted value of y when x is 5 c) Find the predicted value of y when x is 7. d) Find the predicted value of y when x is 10.

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Sum of Squares Total: SST = ( 29 - 2 y y i = ( 29 2 1 y s n - Sum of Squares Due to Regression: SSR = ( 29 - 2 ˆ y y i = ( 29 2 ˆ 1 y s n - Sum of Squares Due to Error: SSE = ( 29 - 2 ˆ i i y y Fact: SST = SSR + SSE e) Calculate SST f) Calculate SSR g) Calculate SSE Coefficient of Determination: r 2 = SST SSR h) Calculate the coefficient of determination.
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