Construct the Multiple Regression Sequence $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 }$

question 66

Multiple Choice

Construct the multiple regression sequence $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 }$ for the following data set:
$\begin{array} { c c c c } y & x _ { 1 } & x _ { 2 } & x _ { 3 } \\31.3 & 50 & 19 & 4.0 \\56.9 & 90 & 38 & 8.0 \\43.1 & 70 & 28 & 6.5 \\41.5 & 70 & 25 & 5.5 \\39.0 & 60 & 26 & 6.5 \\40.9 & 70 & 29 & 5.0 \\35.9 & 60 & 23 & 5.5 \\43.5 & 70 & 28 & 5.5 \\47.9 & 80 & 34 & 6.5 \\33.8 & 70 & 26 & 4.5\end{array}$

• A) \(\hat { y } = 0.3258 + 0.2125 x _ { 1 } + 0.3888 x _ { 2 } + 2.6856 x _ { 3 }\)
• B) \(y = 0.3518 + 0.2129 x _ { 1 } + 0.4167 x _ { 2 } + 2.5798 x _ { 3 }\)
• C) \(y = 2.5798 + 0.4167 x _ { 1 } + 0.2129 x _ { 2 } + 0.3518 x _ { 3 }\)
• D) \(\hat { y } = 2.6856 + 0.3888 x _ { 1 } + 0.2125 x _ { 2 } + 0.3258 x _ { 3 }\)

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Definitions:

Dark Skin

A human skin color that is rich in melanin pigments, particularly eumelanin, often found in populations close to the equator to protect against ultraviolet radiation.

Solar Radiation

The radiant energy emitted by the sun, particularly electromagnetic energy that reaches the Earth.

Melanin

A dark pigment produced in the outer layer of the skin that protects against damaging ultraviolet solar radiation.

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