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

question 47

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, $X _ { 1 } , X _ { 2 } , X _ { 3 }$ $$\begin{array} { c r c c l } Y & X _ { 1 } & X _ { 2 } & X _ { 3 } & \\456 & 9896 & 29.1 & 1 & \\421 & 9680 & 42.3 & 2 & \\653 & 10449 & 29.8 & 3 & \\573 & 10811 & 26.0 & 4 & \text { CORRELATION COEFFICIENTS } \\546 & 10014 & 34.3 & 5 & \\499 & 10293 & 22.7 & 6 & Y / X _ { 1 } = 0.509 \\504 & 9413 & 24.2 & 7 & Y / X _ { 2 } = 0.280 \\611 & 9860 & 31.6 & 8 & Y / X _ { 3 } = 0.930 \\646 & 9782 & 25.6 & 9 & \\789 & 12139 & 37.9 & 10 & \text { COEFFICIENTS OF DETERMINATION } \\773 & 12166 & 33.9 & 11 & \\753 & 9976 & 37.4 & 12 & Y / X _ { 1 } = 0.259 \\852 & 10645 & 27.0 & 13 & Y / X _ { 2 } = 0.079 \\755 & 9738 & 31.5 & 14 & Y / X _ { 3 } = 0.864 \\815 & 9933 & 39.9 & 15 & Y / X _ { 1 } , X _ { 3 } = 0.880 \\902 & 10132 & 25.3 & 16 & Y / X _ { 1 } , X _ { 2 } , X _ { 3 } = 0.884 \\986 & 11145 & 30.4 & 17 & \\909 & 9775 & 32.7 & 18 & \\945 & 9549 & 35.0 & 19 & \\866 & 10077 & 33.8 & 20 & \\1178 & 11550 & 29.4 & 21 & \\1230 & 10600 & 37.1 & 22 & \\1207 & 11280 & 42.9 & 23 & \\968 & 12100 & 32.2 & 24 & \\1118 & 12420 & 30.5 & 25 &\end{array}$$ $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l } \hline \text { Productivity } ( \boldsymbol { x } ) & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \\\hline \text { Dexterity } ( \boldsymbol { y } ) & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75\end{array}$$

• A)\(\hat { y } = 2.36 + 2.03 x\)
• B)\(\hat { y } = 10.7 + 1.53 x\)
• C)\(\hat { y } = 75.3 - 0329 x\)
• D)\(\hat { y } = 5.05 + 1.91 x\)

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