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 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 & \text { 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 & \text { Y/ } X _ { 1 } = 0.259 \\ 852 & 10645 & 27.0 & 13 & \text { YI } X _ { 2 } = 0.079 \\ 755 & 9738 & 31.5 & 14 & Y / X _ { 3 } = 0.864 \\ 815 & 9933 & 39.9 & 15 & \text { Y/ } X _ { 1 } , X _ { 3 } = 0.880 \\ 902 & 10132 & 25.3 & 16 & \text { 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}

\hat { Y } = 57.8 + 0.036 X _ { 1 } + 28.1 X _ { 3 }

\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }

\hat { Y } = 201.7 + 0.40 X _ { 1 } + 22.3 X _ { 3 }

\hat { Y } = 308.6 + 29.9 X _ { 3 }

The Following Residual Plot Is Obtained After a Regression Equation

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