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Chapter 12: Q. 66 (page 721)

66. Can a coefficient of determination be negative? Why or why not?

Short Answer

Expert verified

A coefficient of determination cannot be negative.

Step by step solution

01

Given information

A coefficient of determination can be negative or not.

02

Explanation

A Coefficient of finding R2 is the linear equation utilized for prediction. The coefficient of a conclusion is estimated as follows:
R2=1鈭�SSresSStot

SSres=鈭�i=1n鈥�ei2

SStot=鈭�i=1n鈥�yi鈭�y炉2

where SSres,SStotsum of residuals and the total sum of squares, respectively. Since, r nearer to 1 is that the standard is better.
From the earlier, the coefficient of the conclusion can't be negative. It has values between 0 and 1 . And if theR2 is small, the model used for prediction is not appropriate and requires fixing because it received the wrong predicted values.

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