HW ILR - Chapter 8(SDM Linear Regression 2 Regression...

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Chapter 8 (SDM) Linear Regression 2) Regression Equations x s x y s y r ŷ = b o + b 1 x 30 4 18 6 -0.2 ŷ = 27 –0.3x 100 18 60 10 0.9 ŷ = 10 + 0.5x 4 0.8 50 15 0.8 ŷ = -10 + 15x 6 1.2 18 4 -0.6 ŷ = 30- 2x a) b 1 = rs y /s x = (-0.2)(6)/(4) = b 1 =-0.3 ŷ = b o + b 1 x y = b o + b 1 x 18 = b o + (-0.3)(30) 18 = b o + (-9) b 0 = 27 So, ŷ = 27- 0.3x b) b 1 = rs y /s x = (0.9)(10)/(18) = b 1 =0.5 ŷ = b o + b 1 x y = b o + b 1 x 60 = b o + (0.5)(100) 60 = b o + (50) b 0 = 10 So, ŷ = 10 + 0.5x c) ŷ = b o + b 1 x y = b o + b 1 x 50 = (-10) + (15)x 60 = 15x x = 4 b 1 = rs y /s x r =(s x )(b 1 )/(S y ) (0.8)(15)/(15) r = 0.8 d) ŷ = b o + b 1 x y = b o + b 1 x 18 = (30) - (2)x -12 = -2x x = 6 b 1 = rs y /s x s x = rs y /b 1 (-0.6)(4)/(-2) s x = 1.2

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4) Residuals a. The residual plot has a curved pattern. This indicates that the linear model is not appropriate. The relationship is not linear. b. The residual plot has a fanned pattern that indicates the linear model is not appropriate. The models predicting power increases as the values of the explanatory variable decrease. c. The scattered residual plot indicates that it is an appropriate linear model. 8) Roller Coaster a. The explanatory variable (x) is drop, measured in seconds, and the response variable (y) is duration measured in feet. b. The units of the slope are feet per seconds (ft/s) c. The slope of the line predicting duration from drop should be positive because roller coasters are expected to be fast and have a higher duration.
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