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Use Computer Software to Find the Best Regression Equation to Explain

question 118

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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
- YX1X2X3456989629.11421968042.326531044929.835731081126.045461001434.354991029322.76504941324.27611986031.68646978225.697891213937.9107731216633.911753997637.4128521064527.013755973831.514815993339.9159021013225.3169861114530.417909977532.718945954935.0198661007733.82011781155029.42112301060037.12212071128042.9239681210032.22411181242030.525\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
Y/X1=.509Y/X2=.280Y/X3=.930\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
Y/X1=.259Y/X2=.079Y/X3=.864Y1/X1,X3=.880Y/X1,X2,X3=.884\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}

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Definitions:

Categorical Approach

A method in psychiatry and psychology that classifies mental disorders into specific, distinct categories based on symptomatology.

Mental Disorder

A broad term for conditions affecting mental health, characterized by alterations in thinking, mood, or behavior associated with distress or impaired functioning.

Diagnostic Criteria

A set of guidelines used to determine the presence of a disease or disorder.

Dimensional Approach

An approach in psychology that considers mental disorders along a continuum rather than distinct categories, emphasizing the range of severity and symptoms.

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