Use Computer Software to Find the Best Regression Equation to Explain

question 31

Multiple Choice

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

• A) \(\hat { Y } = - 355 + 14.9 X _ { 1 }\)
• B) \(\hat { Y } = - 442 + 12.1 X _ { 1 } + 3.58 X _ { 2 } - 23.8 X _ { 3 }\)
• C) \(\hat { Y } = - 412 + 13.6 X _ { 1 } + 3.15 X _ { 2 }\)
• D) \(\hat { Y } = - 543 + 12.8 X _ { 1 } + 4.15 X _ { 2 }\)

---

Definitions:

Political Change

Alterations in the governance, policies, or societal structures of a political entity, often leading to significant shifts in power dynamics.

Pro or Con Views

Refers to arguments or opinions in favor of (pro) or against (con) a particular topic, policy, or idea.

Availability Heuristic

A mental shortcut that relies on immediate examples that come to mind when evaluating a specific topic, concept, method, or decision.

Health Risks

Potential factors or behaviors that can lead to illness or adverse health outcomes.