There Are Four Independent Variables $x _ { 1 } , x _ { 2 } , x _ { 3 }$

question 94

Multiple Choice

There are four independent variables, $x _ { 1 } , x _ { 2 } , x _ { 3 }$ , and $x _ { 4 }$ , that might be useful in predicting a response $y$ . A total of $n = 40$ observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to useful. The computer fits all possible one-variable models of the form $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { i } , i = 1,2,3,4$ . The information in the table is provided from the computer printout.
$\begin{array}{lrr}\hline \text { Variable } &{\beta} &{s} \\\hline \mathrm{X} 1 & 2.4 & 0.52 \\\mathrm{X} 2 & -0.2 & 0.03 \\\mathrm{X} 3 & 3.6 & 2.11 \\\mathrm{X} 4 & 0.8 & 0.44 \\\hline\end{array}$

Which independent variable is declared the best one-variable predictor of $y$ ?

• A) \(x _ { 1 }\)
• B) \(x _ { 2 }\)
• C) \(x _ { 3 }\)
• D) \(x _ { 4 }\)

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