Question

The coefficient of determination (r2) tells you
the proportion of total variation that is explained.
whether r has any significance.
that the coefficient of correlation (r) is larger than 1.
that you should not partition the total variation.

Answer 1

The coefficient of determination (r²) tells one the proportion of total variation that is explained.

The coefficient of determination is the proportion of the change in the dependent variable predicted by the independent variable. It is denoted by  r² or R².

The formula for this is given by, $R^2=1-\frac{SSR}{TSS}$. Here, SSR is the sum of the squared regression and TSS is the total sum of squares or sum of total squared.

This helps in evaluating how accurately a statistical model predicts a result.  In simple, it is used to examine how variations in one variable are accounted for variations in another.  In statistics studies, it is used to predict future outcomes or hypotheses testing.

Therefore, the first statement is the correct option.

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