Coefficient of Determination

Coefficient of Determination:

There are some points to determine the Coefficient of Determination:

A) The percent of variation which can be described by the regression equation.
B) The described variation divided by the total variation.
C) The square of r.

What's all this variation stuff is?

Each and every sample consists of some variation in it (except all the values are similar and that is unlikely to occur). The total variation is made up of two portions, the part which can be described by the regression equation and the portion which cannot be described by the regression equation.
 
The ratio of described variation to the total variation is the measure of how good, the regression line is. When the regression line passed via each and every point on the scatter plot precisely, it would be capable to elucidate all the variation. Further the line is from points, the less it is capable to elucidate.

Coefficient of Non-Determination:

It is explained as follows:

a) The percent of variation that is unexplained by regression equation.
b) The unexplained variation divided by total variation
c) 1 - r^2

Standard Error of Estimate:

The coefficient of non-determination was employed in t-test to see when there was significant linear correlation. This was the numerator of standard error formula.

The standard error of estimate is the square root of coefficient of non-determination divided by its degree of freedom.

Se = √(1-r2)/(n-2)

Confidence Interval for y':

The given below works only if the sample size is big. Big in this instance is generally taken to be greater than 100. The maximum error of estimate is provided, and this maximum error of estimate is subtracted from and added up to the estimated value of y.

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