Question

The coefficient of determination measures which of the following? group of answer choices

O the proportion of the variability in y that is accounted for by the linear relationship between x and y.
O the increase (or decrease) in y for each unit increase in x.
O the goodness of fit of a line to a set of data.
O the strength of the linear relationship between x and y.

Answer 1

The coefficient of determination, r², measures the proportion of variablility in y that is explained by the linear relationship with x, represented as a percentage of the variation in y explained by x.

Step-by-step explanation:

The coefficient of determination, often symbolized as r², measures the proportion of the variability in the dependent variable (y) that is accounted for by the linear relationship between the independent variable (x) and the dependent variable (y). It is the square of the correlation coefficient (r), and, when expressed as a percentage, it quantifies how much of the variation in y can be explained by the variation in x using the regression line.

For example, if the correlation coefficient is 0.6631, the coefficient of determination would be r² = 0.6631² = 0.4397. This means that approximately 44 percent of the variation in the final exam grades can be explained by the variation in the grades on the third exam, using the best-fit regression line.