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) \(64.5 \%\)

---

Definitions:

Telephone Interview

A method of conducting an interview over the phone, commonly used in preliminary employment screening or research.

Practise

The act of repeatedly doing or training in something to improve skill or proficiency.

Radically Different Persona

A character or identity that is fundamentally distinct and dissimilar from what is usual or expected, often adopted in specific circumstances.

Corporate Culture

The shared values, beliefs, attitudes, and practices that characterize an organization and guide its employees' behavior.