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Determine R^2 and Adjusted R^2
-A Gym Teacher Uses Three R2\mathrm { R } ^ { 2 }

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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 R2\mathrm { R } ^ { 2 } for the multiple regression model y^=b0+b1x1+b2x2\hat { \mathrm { y } } = \mathrm { b } _ { 0 } + \mathrm { b } _ { 1 } \mathrm { x } _ { 1 } + \mathrm { b } _ { 2 } \mathrm { x } _ { 2 } where x1\mathrm { x } _ { 1 } is Push Ups, x2\mathrm { x } _ { 2 } is Pull Ups, and y\mathrm { y } is the response variable "Rope Climb".
 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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Definitions:

Atomic

Relating to atoms, the smallest constituent unit of ordinary matter that constitutes a chemical element.

Mass Number

The total number of protons and neutrons in an atom's nucleus.

Isotopes

Variants of a particular chemical element that differ in neutron number, and consequently in nucleon number, but have the same number of protons in their nuclei.

Atomic Number

The number of protons found in the nucleus of an atom, which determines the chemical properties of an element and its place in the periodic table.

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