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
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\begin{array} { c c c l c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \mathrm { X } _ { 3 } & \\ 344 & 45.0 & 67.5 & 1 & \text { CORRELATION COEFFICIENTS } \\ 416 & 54.0 & 72.0 & 1 & \mathrm { Y } / \mathrm { X } _ { 1 } = .951 \\ 220 & 41.0 & 70.0 & 2 & \mathrm { Y } / \mathrm { X } _ { 2 } = .789 \\ 360 & 49.0 & 68.5 & 1 & \mathrm { Y } / \mathrm { X } _ { 3 } = - .616 \\ 332 & 44.0 & 73.0 & 1 & \\ 140 & 32.0 & 63.0 & 2 & \\ 436 & 48.0 & 72.0 & 1 & \text { COEFFICIENTS OF DETERMINATION } \\ 132 & 33.0 & 61.0 & 2 & \\ 356 & 48.0 & 64.0 & 2 & \mathrm { Y } _ { 1 } / \mathrm { X } _ { 1 } = .905 \\ 150 & 35.0 & 59.0 & 1 & \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } = .919 \\ 202 & 40.0 & 63.0 & 2 & \mathrm { Y } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } = .927 \\ 365 & 50.0 & 70.5 & 1 & \end{array}

\hat { Y } = - 355 + 14.9 X _ { 1 }

\hat { Y } = - 442 + 12.1 X _ { 1 } + 3.58 X _ { 2 } - 23.8 X _ { 3 }

\hat { Y } = - 412 + 13.6 X _ { 1 } + 3.15 X _ { 2 }

\hat { Y } = - 543 + 12.8 X _ { 1 } + 4.15 X _ { 2 }

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