how do I calculate to get the answer?

Question

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression​ line? About the unexplained​ variation?

r =0.515

Answer 1

Hi Tina!

The linear correlation coefficient is frequently abbreviated as r, while the coefficient of determination is abbreviated as r². As the abbreviations imply, to get from one to the other you simply square your r value.

correlation coefficient = r = 0.515

coefficient of determination = r² = (0.515)²

r²=0.265225 ≈ 0.27

For the second part of the question, the coefficient of determination tells you how much of the variation in y (dependent variable) can be attributed to x (independent variable). This means that approximately 27% of the variation in your data can be explained by your independent variable.