What is the difference between R 2 and Adjusted R 2 ? Read carefully. R 2 will a
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Question
What is the difference between R2 and Adjusted R2? Read carefully.
R2 will always increase as more x variables are added to the model, while Adjusted R2 may decrease if the additional predictive ability of the added variables is not enough to offset the penalty for adding the variables.
R2 will always be less than or equal to 1, and will always decrease with additional x variables. Adjusted R2 can be any number greater than 1, and will always increase with additional x variables.
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R2 will always decrease as more x variables are added to the model, while Adjusted R2 may decrease if the additional predictive ability of the added variables is not enough to offset the penalty for adding the variables.
R2 will always increase as more x variables are added to the model, while Adjusted R2 will decrease if the all of the possible values of each of the x variables are positive.
a)R2 will always increase as more x variables are added to the model, while Adjusted R2 may decrease if the additional predictive ability of the added variables is not enough to offset the penalty for adding the variables.
b)R2 will always be less than or equal to 1, and will always decrease with additional x variables. Adjusted R2 can be any number greater than 1, and will always increase with additional x variables.
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c)R2 will always decrease as more x variables are added to the model, while Adjusted R2 may decrease if the additional predictive ability of the added variables is not enough to offset the penalty for adding the variables.
d)R2 will always increase as more x variables are added to the model, while Adjusted R2 will decrease if the all of the possible values of each of the x variables are positive.
Explanation / Answer
The adjusted R2 has many applications in real life. R2 shows how well terms (data points) fit a curve or line. Adjusted R2 also indicates how well terms fit a curve or line, but adjusts for the number of terms in a model. If you add more and more useless variables to a model, adjusted r-squared will decrease, but if you add more useful variables, adjusted r-squared will increase.
The correct option is:
a) R2 will always increase as more x variables are added to the model, while Adjusted R2 may decrease if the additional predictive ability of the added variables is not enough to offset the penalty for adding the variables.
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