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

question 86

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.



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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Definitions:

Variable

A characteristic, number, or quantity that can change or vary, often used in research to measure and analyze differences or effects.

Experimental Group

A group in a scientific study that receives the treatment or intervention being tested, allowing researchers to measure the effect of the treatment.

Control Group

In experimental research, the group of subjects not exposed to the treatment, used as a benchmark to measure the effect of the treatment group.

Randomization Technique

A method used in experiments to randomly assign subjects to different groups to reduce bias and ensure the groups are comparable.