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

question 131

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
$$\mathrm{Y}=3.9695+1.4577 \mathrm{X} 1-1.7859 \mathrm{X} 2+0.7686 \mathrm{X} 3+0.0777 \mathrm{X} 4$$

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

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

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


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

• A) Yes
• B) No

---

Definitions:

Break-even Sales

The amount of revenue needed to cover total costs, both fixed and variable, with no profit or loss.

Unit Selling Price

The cost for which customers can purchase an individual unit of a product.

Unit Variable Costs

Unit variable costs are the costs that vary directly with the production volume, including costs for materials and labor that change with the level of production or service provision.

Operating Income

Revenue obtained from the main operations of a business, not including the costs of interest and taxes.