3-2 Day 1 The role of r2 in regression

3-2 Day 1 The role of r2 in regression - 2 , is the...

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AP STATISTICS AP STATISTICS LESSON 3 – 3 (DAY 2) LESSON 3 – 3 (DAY 2) The role of r 2 in regression
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Essential Question: Essential Question: How is the r How is the r 2 2 used to determine the used to determine the reliability of a linear regression line? reliability of a linear regression line? To calculate r 2 . To find the SST, the SSE and find the r 2 from them.
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Definitions and Abbreviations Definitions and Abbreviations r 2 = 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
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Exercises Exercises Small r Small r 2 2 and Large r and Large r 2 2 Page 158 : Example 3.10 SMALL r 2 Page 160 : Example 3.11 LARGE r 2
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r r 2 2 in Regression in Regression The coefficient of determination r
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Unformatted text preview: 2 , is the fraction of the variation in the values of y that is explained by least-squares regression of y on x. r 2 = SST - SSE SST Facts about Least-squares Facts about Least-squares Regressions 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 Facts of Regression (continued) (continued) Fact 3. The least-squares regression line always passes through the point (x,y). Fact 4. The square of the correlation, r 2 , is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x....
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3-2 Day 1 The role of r2 in regression - 2 , is the...

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