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

question 13

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

• A) \(\hat { Y } = 57.8 + 0.036 X _ { 1 } + 28.1 X _ { 3 }\)
• B) \(\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }\)
• C) \(\hat { Y } = 201.7 + 0.40 X _ { 1 } + 22.3 X _ { 3 }\)
• D) \(\hat { Y } = 308.6 + 29.9 X _ { 3 }\)

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Definitions:

SSB

Sum of Squares Between groups, a measure used in statistical analysis to quantify the variance among different groups.

SSA

SSA stands for Social Security Administration, a U.S. government agency that administers social security, a social insurance program consisting of retirement, disability, and survivors' benefits.

SSB

Sugar-sweetened beverages, which are drinks that contain added sugars and are often linked to various health issues.

SST

In the context of statistics, typically refers to the total sum of squares in an ANOVA test, measuring the total variation in the data.