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Examples of approximate R2 values

 

 

R2 = 1

Perfect linear relationship between x and y:

100% of the variation in y is explained by variation in x

 

 

 

 

Example

The result of the linear regression is: Y = 0.10 - 0.50 X with a correlation coefficient R = (-0.90).
The fraction of the variance of Y attributable to X is equal to:

  1. (-0.90)
  2. (+0.90)
  3. (+0.81)
  4. (-0.50)
     
Solution

C.
R-squared is the square of the correlation coefficient and measures the fraction of the variance of Y that is attributable to X.R2 = (-0.90)2 = 0.81
 

 






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