12. Regression

In a given dataset, you determine the value of the correlation coefficient to be $r=-0.957$. Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? What about the unexplained variation?

A retail analyst is studying the relationship between the number of in-store promotional displays (x) and weekly sales revenue (y) at 12 store locations. Use the data below and a calculator to find the coefficient of determination.

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

15. r = 0.642"

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

13. r =- 0.450"

The coefficient of determination r^2 is the ratio of which two types of variations? What does r^2 measure? What does 1 - r^2 measure?

What is the coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation? Interpret your answer.

Why might two students have different calculated areas when measuring the same rectangle?