Use Computer Software to Find the Best Multiple Regression Equation $Y$

question 9

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, $X _ { 1 } , X _ { 2 } , X _ { 3 }$ .
$\begin{array}{l}\begin{array}{lll}Y & X_{1} & X_{2} \\15 & 1.2 & 16 \\15 & 1.2 & 16 \\17 & 1.0 & 16 \\6 & 0.8 & 9 \\1 & 0.1 & 1 \\8 & 0.8 & 8 \\10 & 0.8 & 10 \\17 & 1.0 & 16 \\15 & 1.2 & 15 \\11 & 0.7 & 9 \\18 & 1.4 & 18 \\16 & 1.0 & 15 \\10 & 0.8 & 9 \\7 & 0.5 & 5 \\18 & 1.1 & 16\end{array}\begin{array}{c}\text { CORRELATION COEFFICIENT }\\\\Y / X_{1}=0.886\\Y / X_{2}=0.965\\\\\\\text { COEFFICIENTS OF DETERMINATION }\\\\Y / X_{2}=0.932\\Y / X_{2}, X_{1}=0.943\\\end{array}\end{array}$

• A) \(\hat { Y } = 0.42 + 0.99 X _ { 2 }\)
• B) \(\hat { Y } = 1.38 - 5.53 X _ { 1 } + 1.33 X _ { 2 }\)
• C) \(\hat { Y } = 1.25 - 1.55 X _ { 1 } + 5.79 X _ { 2 }\)
• D) \(\hat { Y } = - 0.49 + 14.07 X _ { 1 }\)

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Definitions:

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution without violating any constraints.

T Distribution

A probability distribution that is used to estimate population parameters when the sample size is small and the population variance is unknown.

T-Test Statistic

A statistical measure used to assess the significance of the difference between the mean values of two groups.

Null Hypothesis

In statistical hypothesis testing, it is the hypothesis that there is no significant difference or effect, serving as the default or initial assumption.