Use Computer Software to Find the Best Multiple Regression Equation $Y$

question 113

Multiple Choice

Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, $Y$ , in terms of the independent variables, $X_{1}, X_{2}, X_{3}$ .

$\begin{array}{|cccc|}\hline Y & X_{1} & X_{2} & \\98.6 & 87.4 & 108.5 & \\101.2 & 97.6 & 110.1 & \\102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \\100.9 & 98.2 & 104.3 & \\102.3 & 99.8 & 107.2 & Y / X_{1}=0.850 \\101.5 & 100.5 & 105.8 & Y / X_{2}=0.742 \\101.6 & 103.2 & 107.8 & \\101.6 & 107.8 & 103.4 & \\99.8 & 96.6 & 102.7 & \text { COEFFICIENT OF DETERMINATION } \\100.3 & 88.9 & 104.1 & \\97.6 & 75.1 & 99.2 & \\97.2 & 76.9 & 99.7 & \\97.3 & 84.6 & 102.0 & \\96.0 & 90.6 & 94.3 & \\99.2 & 103.1 & 97.7 & \\100.3 & 105.1 & 101.1 & \\100.3 & 96.4 & 102.3 & \\104.1 & 104.4 & 104.4 & \\105.3 & 110.7 & 108.5 & \\107.6 & 127.1 & 111.3 & \\\hline\end{array}$

• A) \( \hat{Y}=52.6+0.462 X_{2} \)
• B) \( \hat{Y}=48.0+0.398 X_{1}+0.228 X_{2} \)
• C) \( \hat{Y}=57.6+0.153 X_{1}+0.270 X_{2} \)
• D) \( \hat{Y}=58.9+0.612 X_{1} \)

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Definitions:

Primacy Effect

A cognitive phenomenon where items or information presented first are remembered better than those presented later.

Short-term Memory Capacity

The amount of information that can be held in the short-term memory for a brief period, typically regarded as lasting 20 to 30 seconds.

Chunking

A cognitive strategy for organizing information into meaningful groups or chunks to enhance memory and recall.

Parallel Search

A search for information in which several stores or slots of information are simultaneously examined to match to the target.