If you square a correlation coefficient and subtract this number from 1.00, what is the result?
Is it the coefficient of determination?
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yes
Yes, the result of subtracting the square of a correlation coefficient from 1.00 is indeed the coefficient of determination.
To understand why, let's break it down step by step:
1. The correlation coefficient (often denoted as "r") measures the strength and direction of the linear relationship between two variables.
2. When a correlation coefficient is squared (r^2), it represents the proportion of the variability in one variable (dependent variable) that can be explained by the linear relationship with the other variable (independent variable).
3. The coefficient of determination is defined as the proportion of the total variation in the dependent variable that can be accounted for by the independent variable(s). It is represented by the symbol R^2.
4. Since r^2 represents the proportion of variability explained, subtracting it from 1.00 yields the remaining proportion of variability unexplained, which is precisely what R^2 represents.
Therefore, when you subtract the square of the correlation coefficient from 1.00, the result is the coefficient of determination (R^2).