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, $$X _ { 1 } , X _ { 2 } , X _ { 3 }$$ $\begin{array} { c c c c } Y & X _ { 1 } & X _ { 2 } & \ 98.6 & 87.4 & 108.5 & \ 101.2 & 97.6 & 110.1 & \ 102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \ 100.9 & 98.2 & 104.3 & \ 102.3 & 99.8 & 107.2 & Y / X _ { 1 } = 0.850 \ 101.5 & 100.5 & 105.8 & Y X _ { 2 } = 0.742 \ 101.6 & 103.2 & 107.8 & \ 101.6 & 107.8 & 103.4 & \ 99.8 & 96.6 & 102.7 & \text { COEFFICIENT OF DETERMINATION } \ 100.3 & 88.9 & 104.1 & \ 97.6 & 75.1 & 99.2 & \ 97.2 & 76.9 & 99.7 & \ 97.3 & 84.6 & 102.0 & \ 96.0 & 90.6 & 94.3 & \ 99.2 & 103.1 & 97.7 & \ 100.3 & 105.1 & 101.1 & \ 100.3 & 96.4 & 102.3 & \ 104.1 & 104.4 & 104.4 & \ 105.3 & 110.7 & 108.5 & \ 107.6 & 127.1 & 111.3 & \end{array}$
A) $\hat { Y } = 57.6 + 0.153 X _ { 1 } + 0.270 X _ { 2 }$
B) $\hat { Y } = 58.9 + 0.612 X _ { 1 }$
C) $\hat { Y } = 52.6 + 0.462 X _ { 2 }$
D) $\hat { Y } = 48.0 + 0.398 X _ { 1 } + 0.228 X _ { 2 }$

Question

Quizplus · Accepted Answer

Given the complexity of calculating the best multiple regression equation manually, especially without the raw data for $X_3$ and without the software output, it's not feasible to accurately determine the correct regression equation from the options provided. The correct answer would typically be obtained by inputting the data into statistical software and performing a multiple regression analysis, which would consider the relationships between the dependent variable $Y$ and the independent variables $X_1, X_2, X_3$, along with their respective correlation coefficients and other statistical measures.

Use Computer Software to Find the Best Multiple Regression Equation X1,X2,X3X _ { 1 } , X _ { 2 } , X _ { 3 }X1​,X2​,X3​

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