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:

Prices

The financial amount expected, required, or supplied as remuneration for an item.

Income

Money received on a regular basis from work, property, investments, business ventures, and other sources, used to fund consumption and savings.

Laspeyres Index

A price index used to measure the change in the cost of purchasing a fixed basket of goods and services of the same type and quantity over time.

Prices

The amounts of money required to purchase goods or services, setting the economic value of said goods or services in the market.