Use Computer Software to Find the Best Regression Equation to Explain

question 118

Multiple Choice

Use computer software to find the best regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3
- $\begin{array}{cccc}Y & X_{1} & X_{2} & X_{3} \\456 & 9896 & 29.1 & 1 \\421 & 9680 & 42.3 & 2 \\653 & 10449 & 29.8 & 3 \\573 & 10811 & 26.0 & 4 \\546 & 10014 & 34.3 & 5 \\499 & 10293 & 22.7 & 6\\504 & 9413 & 24.2 & 7 \\611 & 9860 & 31.6 & 8 \\646 & 9782 & 25.6 & 9 \\789 & 12139 & 37.9 & 10 \\773 & 12166 & 33.9 & 11 \\753 & 9976 & 37.4 & 12 \\852 & 10645 & 27.0 & 13\\755 & 9738 & 31.5 & 14 \\815 & 9933 & 39.9 & 15 \\902 & 10132 & 25.3 & 16 \\986 & 11145 & 30.4 & 17 \\909 & 9775 & 32.7 & 18\\945 & 9549 & 35.0 & 19 \\866 & 10077 & 33.8 & 20 \\1178 & 11550 & 29.4 & 21 \\1230 & 10600 & 37.1 & 22 \\1207 & 11280 & 42.9 & 23 \\968 & 12100 & 32.2 & 24 \\1118 & 12420 & 30.5 & 25\end{array}$
CORRELATION COEFFICIENTS
$\begin{array}{l}\mathrm{Y} / \mathrm{X}_{1}=.509 \\\mathrm{Y} / \mathrm{X}_{2}=.280 \\\mathrm{Y} / \mathrm{X}_{3}=.930\end{array}$
COEFFICIENTS OF DETERMINATION
$\begin{array}{c}\mathrm{Y} / \mathrm{X}_{1}=.259 \\\mathrm{Y} / \mathrm{X}_{2}=.079 \\\mathrm{Y} / \mathrm{X}_{3}=.864 \\\mathrm{Y}_{1} / \mathrm{X}_{1}, \mathrm{X}_{3}=.880 \\\mathrm{Y} / \mathrm{X}_{1}, \mathrm{X}_{2}, \mathrm{X}_{3}=.884\end{array}$

• A) \(\hat { \mathrm { Y } } = 308.6 + 29.9 \mathrm { X } _ { 3 }\)
• B) \(\hat { \mathrm { Y } } = 57.8 + 0.036 \mathrm { X } _ { 1 } + 28.1 \mathrm { X } _ { 3 }\)
• C) \(\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }\)
• D) \(\hat { Y } = 201.7 + 0.40 \mathrm { X } _ { 1 } + 22.3 \mathrm { X } _ { 3 }\)

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Definitions:

Spontaneous Recovery

The reappearance of a previously extinguished conditioned response after a period without exposure to the conditioned stimulus.

Stimulus Generalization

The process by which a conditioned response becomes associated with stimuli that are similar but not identical to the original conditioned stimulus.

Conditioned Response

A learned response to a previously neutral stimulus that has been repeatedly presented along with an unconditioned stimulus.

Heredity

The transmission of physical or mental traits from one generation to the next through genetics.