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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