1. AP STATISTICS LESSON 3 – 3 (DAY 2)
The role of r2 in regression

2. Essential Question: How is the r2 used to determine the reliability of a linear regression line?
To calculate r2.
To find the SST, the SSE and find the r2 from them.

3. Definitions and Abbreviations
r2 = coefficient of determination ( The proportion of the total sample variability that is explained by the least-squares regression of y on x.
LSRL – Least squares regression line.
SST – (Total Sum of Squares)
SST = ∑ ( y – y )2
SSE – (Sum of squares of errors)
SSE = ∑ ( y – ŷ)2

4. Exercises Small r2 and Large r2
Page 158: Example SMALL r2
Page 160: Example LARGE r2

5. r2 in Regression
The coefficient of determination r2, is the fraction of the variation in the values of y that is explained by least-squares regression of y on x.
r2 = SST - SSE
SST

6. Facts about Least-squares Regressions
Fact 1: The distinction between explanatory and response variable is essential in regression.
Fact 2: There is a close connection between correlation and the slope of the least-squares line. A change of one standard deviation of x corresponds to a change of r standard deviations in y.

7. Facts of Regression (continued)
Fact 3. The least-squares regression line always passes through the point ( x, y ).
Fact 4. The square of the correlation, r2, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.