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# lecture21 - Lecture XXI–Simple Linear Regression...

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Unformatted text preview: Lecture XXI–Simple Linear Regression Statistical Methods I STAT 515 University of South Carolina April 08, 2010 Instructor: Ou Zhao Reading output from statistical computing packages ◮ Major statistical software packages, like R, Minitab, SPSS, will report a two-tailed p-value for each of the β-parameters in the regression fitting. For example, in simple linear regression, the p-value for the two-sided test H : β 1 = 0 versus H a : β 1 negationslash = 0 is given on the printout. If you want to perform a one-sided test of hypothesis, you need to make the adjustment. ◮ Upper-tailed test H a : β 1 > 0, p-value= p / 2 if the observed t > 0, and 1 − p / 2 if t < 0. ◮ Lower-tailed test H a : β 1 < 0, p-value= p / 2 if the observed t < 0, and 1 − p / 2 if t > 0. How about confidence interval for β 1 ? ◮ A 100(1 − α )% confidence interval for the simple linear regression slope is given by ˆ β 1 ± t α/ 2 s ˆ β 1 where the estimated standard error of ˆ β 1 is computed as s ˆ β 1 = s √ SS xx and t α/ 2 is based on (n-2) degrees of freedom. Applying to the drug reaction time example...
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lecture21 - Lecture XXI–Simple Linear Regression...

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