What is the relationship between the Coefficient of Determination and the coefficient of correlation?

Coefficient of Correlation (r):

1. It measures the strength and the direction of a linear relationship between two variables (x and y) with possible values between -1 and 1.
2. Positive Correlation: It indicates that two variables are in perfect harmony. They rise and fall together. +1 is perfect +ve correlation
3. Negative Correlation: It indicates that two variables are perfect opposites. One goes up and other goes down. -1 is perfect -ve correlation
4. No correlation: If there is no linear correlation or a weak linear correlation, r is close to 0.

Coefficient of determination (r2):

1. Coefficient of determination (r2) = Coefficient of Correlation (r) x Coefficient of Correlation (r)
2. It provides percentage variation in y which is explained by all the x variables together
3. Its value is (usually) between 0 and 1 and it indicates strength of Linear Regression model
4. Higher the R2 value, data points are less scattered so it is a good model. Lesser the R2 value is more scattered the data points.

It can also be calculated as below:

R2 = 1 — (RSS/TSS)

Where

RSS = Residual Sum of Square

TSS = Total Sum of Square (It’s square of (actual value — average value))

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