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

question 58

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
$$\mathrm { Y } = 4.7712 + 0.2662 \mathrm { X } 1 + 1.2710 \mathrm { X } 2 - 1.1349 \mathrm { X } 3 - 1.8545 \mathrm { X } 4$$
$$\mathrm { S } = 2.8844 \quad \mathrm { R } - \mathrm { Sq } = 49.6 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 43.9 \%$$
$\begin{array}{l}\text { Analysis of Variance }\\\begin{array}{lcccrl}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\\text { Regression } & 4 & 624.2 & 156.1 & 9.8797 & 0.003 \\\text { Residual Error } & 40 & 633.7 & 15.8 & & \\\text { Total } & 44 & 1257.9 & & &\end{array}\end{array}$
It is desired to drop one of the explanatory variables. Which of the following is tl appropriate action?

• A) Drop \(x _ { 1 }\), then see whether adjusted \(R ^ { 2 }\) increases
• B) Drop \(x _ { 1 }\), then see whether \(R ^ { 2 }\) increases
• C) Drop \(x _ { 4 }\), then see whether adjusted \(R ^ { 2 }\) increases
• D) Drop \(x _ { 4 }\), then see whether \(R ^ { 2 }\) increases ost

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Definitions:

Parameter

A numerical characteristic of a population, such as its mean or variance, which is typically unknown and estimated from sample data.

Binomial Distributions

A type of probability distribution that describes the number of successes in a fixed number of binary (yes/no) experiments.

Discrete Random Variables

Variables in statistics that can take on a countable number of distinct values and are not continuous.

Simple Random Sample

A subset of individuals chosen from a larger set such that every individual has an equal chance of being selected.