Determine R^2 and Adjusted R^2
-A Gym Teacher Uses Three $R ^ { 2 }$

question 57

Multiple Choice

Determine R^2 and Adjusted R^2
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in his class. He records the number of push ups each student is able to do in 2 minutes, the number of pull ups each student is able to do in 2 minutes, and the time (in seconds) for each student to climb a rope. The data are shown in the table. The teacher wonders whether the number of push ups and the number of pull ups would be good predictors of the time to climb the rope. Determine the adjusted $R ^ { 2 }$ for the multiple regression model $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ where $x _ { 1 }$ is Push Ups, $x _ { 2 }$ is Pull Ups, and $y$ is the response variable "Rope Climb".

• A) \(82.3 \%\)
• B) \(86.2 \%\)
• C) \(92.8 \%\)
• D) \(74.5 \%\)

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Definitions:

Experiential Process

Learning through direct experience or doing, characterized by exploration and active participation.

Cognitive Control

The ability of the mind to regulate its own processes in directing attention, making decisions, and inhibiting unwanted behaviors or thoughts.

Electrical Signals

Impulses used for communication within organisms, particularly in the nervous system and muscles.

Stereotypic Thoughts

Simplified and generalized beliefs about a group of people that often underlie prejudiced attitudes.