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The percentage of variability in the dependent variable explained by an independent variable is called the

a. coefficient of regression.
b. coefficient of correlation.
c. coefficient of variation.
d. coefficient of determination.

User Trevir
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Final answer:

The coefficient of determination, denoted as r², represents the percentage of variability in the dependent variable explained by an independent variable, indicating how well the data fits a statistical model.

Step-by-step explanation:

The percentage of variability in the dependent variable explained by an independent variable is called the coefficient of determination. This term is represented by r², which is the square of the coefficient of correlation (represented by r). When r is positive, there is a positive association between the variables; when r is negative, there is an inverse association. The correlation coefficient measures the strength of the linear relationship between two variables. The closer the correlation coefficient is to 1 or -1, the stronger the relationship.

To illustrate, consider a scenario where we are looking at the relationship between study time (independent variable x) and test scores (dependent variable y). If the correlation coefficient is r = 0.7, then the coefficient of determination is r² = 0.49 or 49%. This indicates that 49% of the variability in test scores can be explained by the amount of time spent studying.

User Paranoidhominid
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