The Standard Deviation of the Regression Slope The standard error of the

The standard deviation of the regression slope the

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The Standard Deviation of the Regression Slope The standard error of the regression slope coefficient (b 1 ) is estimated by n x) ( x s ) x (x s s 2 2 ε 2 ε b 1 where: = Estimate of the standard error of the least squares slope = Sample standard error of the estimate 1 b s 2 n SSE s ε
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Inference about the Slope: t Test t test for a population slope Is there a linear relationship between x and y? Null and alternative hypotheses H 0 : β 1 = 0 (no linear relationship) H 1 : β 1 0 (linear relationship does exist) Test statistic 1 b 1 1 s β b t 2 n d.f. where: b 1 = Sample regression slope coefficient β 1 = Hypothesized slope s b1 = Estimator of the standard error of the slope
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