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

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.

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

Exercises Small r2 and Large r2 Page 158: Example 3.10 SMALL r2 Page 160: Example 3.11 LARGE r2

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

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.

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.