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:

Demand for Inventoried Items

The need or desire for products or goods that are kept in stock for sale or distribution.

Reductions

Refers to decreases or cuts in quantities, capacities, workforce, costs, or other financial or operational metrics as a strategic or cost-saving measure.

Total Purchases

The aggregate amount of goods and services bought over a certain period of time.

Percentage of Sales

A financial metric or approach calculating a certain cost or investment as a proportion of sales revenue, useful in budgeting and analysis.