Use Computer Software to Find the Best Multiple Regression Equation $X _ { 1 } , X _ { 2 } , X _ { 3 }$

question 5

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. $X _ { 1 } , X _ { 2 } , X _ { 3 }$
$\begin{array} { c c c } Y & X _ { 1 } & X _ { 2 } \\15 & 1.2 & 16 \\15 & 1.2 & 16 \\17 & 1.0 & 16 \\6 & 0.8 & 9 \\1 & 0.1 & 1 \\8 & 0.8 & 8 \\10 & 0.8 & 10 \\17 & 1.0 & 16 \\15 & 1.2 & 15 \\11 & 0.7 & 9 \\18 & 1.4 & 18 \\16 & 1.0 & 15 \\10 & 0.8 & 9 \\7 & 0.5 & 5 \\18 & 1.1 & 16\end{array}$
CORRELATION COEFFICIENT
$\begin{array} { l } \text { Y/ } X _ { 1 } = 0.886 \\\text { Y/ } X _ { 2 } = 0.965\end{array}$
COEFFICIENTS OF DETERMINATION
$\begin{array} { c } \text { Yl } X _ { 2 } = 0.932 \\Y l X _ { 2 } , X _ { 1 } = 0.943\end{array}$

• A) \(\hat { Y } = 0.42 + 0.99 X _ { 2 }\)
• B) \(\hat { Y } = 1.38 - 5.53 X _ { 1 } + 1.33 X _ { 2 }\)
• C) \(\hat { Y } = 1.25 - 1.55 X _ { 1 } + 5.79 X _ { 2 }\)
• D) \(\hat { Y } = - 0.49 + 14.07 X _ { 1 }\)

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Definitions:

Artificial Atmosphere

A man-made environment that replicates the conditions of a natural atmosphere, often used in space exploration or controlled scientific experiments.

Laboratory Experiments

Controlled tests or investigations conducted in a lab setting where variables are closely controlled to explore scientific processes or effects.

Internal Validity

The extent to which a research study can demonstrate that a causal relationship exists between the independent and dependent variables, free from confounding variables.

External Validity

The degree to which a study's findings can be applied to other contexts and different individuals.