coefficient_of_determination_r

Or that can be explained by the linear relationship

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Unformatted text preview: at can be “explained” by the linear relationship between x and y). relationship Coefficient of Determination, r Coefficient 2 r2 is useful because: iit gives the proportion of the variance t (fluctuation) of one variable that is predictable from the other variable predictable explains how much of the variability in explains the y''s can be explained by the fact that s they are related to x Let’s look at a formula Let’s We find the total variation in y (SSTotal) SSTotal = Σ(yi – ybar)² SSTotal ybar)² Is also called SSM (Sum of Squares about the Is mean) mean) Is the variation around the mean…looks like Is variance variance Formula continued Formula We then find the Sum of Squared We Residuals (SSR) Residuals SSR = Σ(yi – ŷi)² SSR Is also called SSE or “sum of squares of error” This is sometimes referred to as a measure of This the “unexplained” variation. Or the amount of variation in y that cannot be attributed to the linear relationship between x and y linear Formula continued This gives us r² = 1 – (SSR / SSTotal) If I multiply by 100, I get the percentage of If y variation attributable to the approximate linear rel...
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This document was uploaded on 03/30/2014 for the course MATH AP Statist at Richard Montgomery High.

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