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

question 125

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, $\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 }$
- $\begin{array} { c c c c c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \mathrm { X } _ { 3 } & \\344 & 45.0 & 67.5 & 1 & \text { CORRELATION COEFFICIENTS } \\416 & 54.0 & 72.0 & 1 & \mathrm { Y } / \mathrm { X } _ { 1 } = 0.951 \\220 & 41.0 & 70.0 & 2 & \mathrm { Y } / \mathrm { X } _ { 2 } = 0.789 \\360 & 49.0 & 68.5 & 1 & \mathrm { Y } / \mathrm { X } _ { 3 } = - 0.616 \\332 & 44.0 & 73.0 & 1 & \\140 & 32.0 & 63.0 & 2 & \mathrm { Y } \\436 & 48.0 & 72.0 & 1 & \mathrm { COEFFICIENTS } \mathrm { OF } \mathrm { DETERMINATION } \\132 & 33.0 & 61.0 & 2 & \mathrm { X } _ { 1 } = 0.905 \\356 & 48.0 & 64.0 & 2 & \mathrm { Y } _ { 1 } , \mathrm { X } _ { 2 } = 0.919 \\150 & 35.0 & 59.0 & 1 & \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } = 0.927 \\202 & 40.0 & 63.0 & 2 & \\365 & 50.0 & 70.5 & 1 &\end{array}$

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

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Definitions:

Marginal Cost

Additional costs associated with the production of one more unit of a product or service.

Monopolistically Competitive

A market structure where many companies sell products that are similar but not identical, allowing for competition based on quality, price, and marketing.

Monopolistic Competition

A market structure in which many firms sell products that are similar but not identical, allowing for some degree of market power.

Product Differentiation

The process of distinguishing a product or service from others in the market to make it more attractive to a particular target market.