coefficient_of_determination_r

Linear the book uses the formula r ssm sse ssm r

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Unformatted text preview: ationship between x and y. linear The book uses the formula: r² = (SSM – SSE) / SSM r² Couple of Examples: Couple The variation of each observation (y) from ŷ is small. ŷ “explains” the variation in y very well High r, high r² The variation of each observation (y) from ŷ is not really small. ŷ doesn’t “explain” the variation in y as well. Poor r, poor r² Example Example Suppose from our strong example that Suppose r = .9 then r² = .81 This means that 81% of the variation in the y This variable is accounted for by the linear relationship between x and y relationship Suppose the other model: r = -.4 then r² = .16 This means that only 16% of the variation in the This y variable is accounted for by the linear relationship relationship Some points Some Always use in context Must interpret the r² with our sentence. Do Must not say: not The regression equation can predict 81% of The the data points the 81% of data points lie on the LSRL LSRL accounts for 81% of the data points Properties of r Properties 2 Prope...
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