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

question 70

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 $\mathrm { R } ^ { 2 }$ for the multiple regression model $\hat { \mathrm { y } } = \mathrm { b } _ { 0 } + \mathrm { b } _ { 1 } \mathrm { x } _ { 1 } + \mathrm { b } _ { 2 } \mathrm { x } _ { 2 }$ where $\mathrm { x } _ { 1 }$ is Push Ups, $\mathrm { x } _ { 2 }$ is Pull Ups, and $\mathrm { y }$ is the response variable "Rope Climb".

• A) \(86.2 \%\)
• B) \(82.3 \%\)
• C) \(92.8 \%\)
• D) \(64.5 \%\)

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