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

Question 117

Multiple Choice

The following MINITAB output presents a multiple regression equation y^=b0+b1x1+\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b2x2+b3x3+b4x4b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }
The regression equation is
Y=3.9695+1.4577X11.7859X2+0.7686X3+0.0777X4\mathrm{Y}=3.9695+1.4577 \mathrm{X} 1-1.7859 \mathrm{X} 2+0.7686 \mathrm{X} 3+0.0777 \mathrm{X} 4

 Predictor  Coef  SE Coef  T  P  Constant 3.96950.87850.92990.327 X1 1.45770.60343.51070.003 X2 1.78590.73023.11480.005 X3 0.76860.67321.92940.088 X4 0.07770.75691.07820.352\begin{array}{lllll}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\\text { Constant } & 3.9695 & 0.8785 & 0.9299 & 0.327 \\\text { X1 } & 1.4577 & 0.6034 & 3.5107 & 0.003 \\\text { X2 } & -1.7859 & 0.7302 & -3.1148 & 0.005 \\\text { X3 } & 0.7686 & 0.6732 & 1.9294 & 0.088 \\\text { X4 } & 0.0777 & 0.7569 & -1.0782 & 0.352\end{array}

S=2.2610RSq=51.5%RSq(adj) =44.8%\mathrm{S}=2.2610 \quad \mathrm{R}-\mathrm{Sq}=51.5 \% \mathrm{R}-\mathrm{Sq}(\mathrm{adj}) =44.8 \%

 Analysis of Variance  Source  DF  SS  MS  F P  Regression 41148.7287.29.00310.003 Residual Error 341083.931.9 Total 382232.6\begin{array}{l}\text { Analysis of Variance }\\\begin{array}{lcccrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\\text { Regression } & 4 & 1148.7 & 287.2 & 9.0031 & 0.003 \\\text { Residual Error } & 34 & 1083.9 & 31.9 & & \\\text { Total } & 38 & 2232.6 & & & \\\hline\end{array}\end{array}


Is the model useful for prediction? Use the α=0.05\alpha = 0.05 level.


A) Yes
B) No

Correct Answer:

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