Question

what are the differences in the interpretation of r^2 and R^2 ?

Answer 1

There there is no difference between r​​​​​​2  and R​​​​​​2

Coefficient of determination is denoted by R² or r² and pronounced "R squared". It is the proportion of the variance in the dependent variable (y) explained by independent variable(x) .

It is square of correlation coefficient between independent variable and dependent variable= (correlation)^2.

It is used in regression model context tells about the amount of variability in y that is explained by the model.

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