Discussion
In a two variable regression Y is dependent variable and X is independent variable. The correlation coefficient between Y and X is 0.6. For this which of the following result is correct ?
Answer: A
The coefficient of determination is the square of the correlation coefficient, so it is 0.6 x 0.6 = 0.36. Thus 36 per cent of the variation in Y is explained by X.
\[ R^2 = r^2 = (0.6)^2 = 0.36 \]60 per cent would be the figure if r were used and not squared, which is a common error, and 6 per cent has no basis in the calculation. So the first option is right. The remaining 64 per cent is explained by other factors and the disturbance term, so the model does not explain the whole variation.
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