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

question 77

Multiple Choice

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$
The regression equation is
$$\mathrm { Y } = 2.5919 - 1.3391 \mathrm { X } 1 + 0.6212 \mathrm { X } 2 + 1.6435 \mathrm { X } 3 + 1.4269 \mathrm { X } 4$$
$\begin{array}{lllll}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\\text { Constant } & 2.5919 & 0.6269 & 1.1668 & 0.337 \\\text { X1 } & -1.3391 & 0.6716 & 3.5190 & 0.002 \\\text { X2 } & 0.6212 & 0.8488 & -3.2848 & 0.004 \\\text { X3 } & 1.6435 & 0.7934 & 1.8821 & 0.090 \\\text { X4 } & 1.4269 & 0.7679 & -0.9879 & 0.345\end{array}$

$\mathrm{S}=2.8912 \quad \mathrm{R}-\mathrm{Sq}=55.3 \% \mathrm{R}-\mathrm{Sq}(\mathrm{adj}) =46.4 \%$

$\begin{array}{l}\text { Analysis of Variance }\\\begin{array}{lcccrl}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\\text { Regression } & 4 & 735.9 & 184.0 & 7.7311 & 0.003 \\\text { Residual Error } & 25 & 594.6 & 23.8 & & \\\text { Total } & 29 & 1330.5 & & & \\\hline\end{array}\end{array}$



Let $\beta _ { 3 }$ be the coefficient $X 3$ Test the hypothesis $H _ { 0 } : \beta _ { 3 } = 0$ versus $H _ { 1 } : \beta 3 \neq 0$ at the $\alpha = 0.05 \text { level. }$ What do you conclude?

• A) Do not reject \(H _ { 0 }\)
• B) Reject \(H _ { 0 }\)

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