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

question 14

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, $\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 }$
- $\begin{array} { c c c c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \\ 98.6 & 87.4 & 108.5 & \\ 101.2 & 97.6 & 110.1 & \\ 102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \\ 100.9 & 98.2 & 104.3 & \mathrm { Y } / \mathrm { X } _ { 1 } = 0.850 \\ 102.3 & 99.8 & 107.2 & \mathrm { Y } / \mathrm { X } _ { 2 } = 0.742 \\ 101.5 & 100.5 & 105.8 & \\ 101.6 & 103.2 & 107.8 & \\ 101.6 & 107.8 & 103.4 & \mathrm { Y } / \mathrm { X } _ { 1 } = 0.723 \\ 99.8 & 96.6 & 102.7 & \mathrm { Y } _ { 2 } = 0.550 \\ 100.3 & 88.9 & 104.1 & \mathrm { Y } _ { 1 } , \mathrm { X } _ { 2 } = 0.867 \\ 97.6 & 75.1 & 99.2 & \\ 97.2 & 76.9 & 99.7 & \\ 97.3 & 84.6 & 102.0 & \\ 96.0 & 90.6 & 94.3 & \\ 99.2 & 103.1 & 97.7 & \\ 100.3 & 105.1 & 101.1 & \\ 100.3 & 96.4 & 102.3 & \\ 104.1 & 104.4 & 104.4 & \\ 105.3 & 110.7 & 108.5 & \\ 107.6 & 127.1 & 111.3 & \end{array}$

• A) \(\hat { Y } = 57.6 + 0.153 X _ { 1 } + 0.270 X _ { 2 }\)
• B) \(\hat { \mathrm { Y } } = 52.6 + 0.462 \mathrm { X } _ { 2 }\)
• C) \(\hat { \mathrm { Y } } = 48.0 + 0.398 \mathrm { X } _ { 1 } + 0.228 \mathrm { X } _ { 2 }\)
• D) \(\hat { \mathrm { Y } } = 58.9 + 0.612 \mathrm { X } _ { 1 }\)

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Definitions:

Circular Argument

A logical fallacy in which the conclusion is supported by premises that assume the truth of the conclusion instead of providing evidence for it.

Hedonic Adaptation

The observed process of people returning to a set level of happiness despite major positive or negative events or life changes.

Natural Selection

A mechanism of evolution where organisms better adapted to their environment tend to survive and produce more offspring, shaping the genetics of populations.

Pleasurable Events

Activities or occurrences that induce a state of enjoyment or happiness.