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The Following MINITAB Output Presents a Multiple Regression Equatior y^\hat { y }

Question 47

Multiple Choice

The following MINITAB output presents a multiple regression equatior y^\hat { y } =b0+b1x1+b2x2+b3x3+b4x4

The regression equation is
Y=2.59191.3391X1+0.6212X2+1.6435X3+1.4269X4\mathrm { Y } = 2.5919 - 1.3391 \mathrm { X } 1 + 0.6212 \mathrm { X } 2 + 1.6435 \mathrm { X } 3 + 1.4269 \mathrm { X } 4

 Predictor  Coef  SE Coef  T  P  Constant 2.59190.62691.16680.337 X1 1.33910.67163.51900.002 X2 0.62120.84883.28480.004 X3 1.64350.79341.88210.090 X4 1.42690.76790.98790.345\begin{array}{lllll}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\\text { Constant } & 2.5919 & 0.6269 & 1.1668 & 0.337 \\\text { X1 } & -1.3391 & 0.6716 & 3.5190 & 0.002 \\\text { X2 } & 0.6212 & 0.8488 & -3.2848 & 0.004 \\\text { X3 } & 1.6435 & 0.7934 & 1.8821 & 0.090 \\\text { X4 } & 1.4269 & 0.7679 & -0.9879 & 0.345\end{array}

 The following MINITAB output presents a multiple regression equatior  \hat { y } =b<sub>0</sub>+b<sub>1</sub>x<sub>1</sub>+b<sub>2</sub>x<sub>2</sub>+b<sub>3</sub>x<sub>3</sub>+b<sub>4</sub>x<sub>4</sub>  The regression equation is  \mathrm { Y } = 2.5919 - 1.3391 \mathrm { X } 1 + 0.6212 \mathrm { X } 2 + 1.6435 \mathrm { X } 3 + 1.4269 \mathrm { X } 4    \begin{array}{lllll} \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 2.5919 & 0.6269 & 1.1668 & 0.337 \\ \text { X1 } & -1.3391 & 0.6716 & 3.5190 & 0.002 \\ \text { X2 } & 0.6212 & 0.8488 & -3.2848 & 0.004 \\ \text { X3 } & 1.6435 & 0.7934 & 1.8821 & 0.090 \\ \text { X4 } & 1.4269 & 0.7679 & -0.9879 & 0.345 \end{array}        \text { Analysis of Variance }   \begin{array}{lccccc} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 4 & 735.9 & 184.0 & 7.7311 & 0.003 \\ \text { Residual Error } & 25 & 594.6 & 23.8 & & \\ \text { Total } & 29 & 1,330.5 & & & \\ \hline \end{array}  Let  \beta _ { 3 }  be the coefficient  X _ { 3 }  Test the hypothesis  H _ { 0 } : \beta _ { 3 } = 0   versus  H _ { 1 } : \beta _ { 3 } \neq 0 \text { at the } \alpha = 0.05  level. What do you conclude? A)  Reject H<sub>0</sub> B)  Do not reject H<sub>0</sub>


 Analysis of Variance \text { Analysis of Variance }
 Source  DF  SS  MS  F  P  Regression 4735.9184.07.73110.003 Residual Error 25594.623.8 Total 291,330.5\begin{array}{lccccc}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { Regression } & 4 & 735.9 & 184.0 & 7.7311 & 0.003 \\\text { Residual Error } & 25 & 594.6 & 23.8 & & \\\text { Total } & 29 & 1,330.5 & & & \\\hline\end{array}
Let β3\beta _ { 3 } be the coefficient X3X _ { 3 } Test the hypothesis H0:β3=0H _ { 0 } : \beta _ { 3 } = 0 versus H1:β30 at the α=0.05H _ { 1 } : \beta _ { 3 } \neq 0 \text { at the } \alpha = 0.05 level. What do you conclude?


A) Reject H0
B) Do not reject H0

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