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The Following MINITAB Output Presents a Multiple Regression Equation y^=b0+b1x1+b2x2+\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } +

Question 45

Multiple Choice

The following MINITAB output presents a multiple regression equation y^=b0+b1x1+b2x2+\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } + +b4x4+ b _ { 4 } x _ { 4 } .
The regression equation is
Y=5.3535+0.7929X10.8918X2+0.5297X31.7948X4\mathrm { Y } = 5.3535 + 0.7929 \mathrm { X } 1 - 0.8918 \mathrm { X } 2 + 0.5297 \mathrm { X } 3 - 1.7948 \mathrm { X } 4
 Predictor  Coef  SE Coef  T  P  Constant 5.35350.72400.87710.338 X1 0.79290.79863.30730.002 X2 0.89180.82082.93540.009 X3 0.52970.89801.94580.083 X4 1.79480.64611.02620.340\begin{array}{lllll}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\\text { Constant } & 5.3535 & 0.7240 & 0.8771 & 0.338 \\\text { X1 } & 0.7929 & 0.7986 & 3.3073 & 0.002 \\\text { X2 } & -0.8918 & 0.8208 & -2.9354 & 0.009 \\\text { X3 } & 0.5297 & 0.8980 & 1.9458 & 0.083 \\\text { X4 } & -1.7948 & 0.6461 & -1.0262 & 0.340\end{array}

 The following MINITAB output presents a multiple regression equation  \hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } +   + b _ { 4 } x _ { 4 } . The regression equation is  \mathrm { Y } = 5.3535 + 0.7929 \mathrm { X } 1 - 0.8918 \mathrm { X } 2 + 0.5297 \mathrm { X } 3 - 1.7948 \mathrm { X } 4   \begin{array}{lllll} \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 5.3535 & 0.7240 & 0.8771 & 0.338 \\ \text { X1 } & 0.7929 & 0.7986 & 3.3073 & 0.002 \\ \text { X2 } & -0.8918 & 0.8208 & -2.9354 & 0.009 \\ \text { X3 } & 0.5297 & 0.8980 & 1.9458 & 0.083 \\ \text { X4 } & -1.7948 & 0.6461 & -1.0262 & 0.340 \end{array}       \text { Analysis of Variance }   \begin{array}{lccccc} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 4 & 1,188.8 & 297.2 & 7.7396 & 0.003 \\ \text { Residual Error } & 31 & 1,190.1 & 38.4 & & \\ \text { Total } & 35 & 2,378.9 & & & \\ \hline \end{array}   b<sub>3</sub>x<sub>3</sub> What percentage of the variation in y is explained by the model? A)  50.0% B)  42.3% C)  0.3% D)  7.7396%

 Analysis of Variance \text { Analysis of Variance }
 Source  DF  SS  MS  F  P  Regression 41,188.8297.27.73960.003 Residual Error 311,190.138.4 Total 352,378.9\begin{array}{lccccc}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { Regression } & 4 & 1,188.8 & 297.2 & 7.7396 & 0.003 \\\text { Residual Error } & 31 & 1,190.1 & 38.4 & & \\\text { Total } & 35 & 2,378.9 & & & \\\hline\end{array}
b3x3 What percentage of the variation in y is explained by the model?


A) 50.0%
B) 42.3%
C) 0.3%
D) 7.7396%

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