For a correlation coefficient r between two variables the va

For a correlation coefficient r between two variables, the value r² measures how much differences of values for one variable are accounted for by the differences of values in the other. For r² = 0, we say that one variable \"explains\" 0% of the other variable (no relationship observed); for r² = 1, one variable \"explains\" 100% of the other. Which value of r corresponds to a situation in which one variable \"explains\" less than 50% of the other variable?

Solution

Regression involves the determination of the degree of relationship in the patterns of variation of two or more variables through the calculation of the coefficient of correlation, r. The value of r can vary between 1.0, perfect correlation, and -1.0, perfect negative correlation.The coefficient of determination, r², is a measure of how well the variation of one variable explains the variation of the other, and corresponds to the percentage of the variation explained by a best-fit regression line which is calculated for the data.

R^2 is always between 0 and 100%:

r^2 < 50 % means not much of relationship between the two , fairly unpredictable