CONFIDENCE INTERVALS FOR REGRESSION COEFFICIENTS


The sample values for the slope and intercept are our best guesses for the population values. However, we know it is unlikely that they are exactly on target. As we have discussed before, it is possible to calculate a confidence interval for the population value. A confidence interval is a range of values that, with a designated likelihood , contains the unknown population value. To obtain 95% confidence intervals for the slope and intercept using for example the SPSS/PC software we identify the command REGRESSION, but we must add an additional specification to the command. It is called the STATISTICS subcommand, and it tells the system what values we want to see printed. That is all. The output is going to give us not only the line of the regression but also the confidence intervals.

Remember what 95% confidence means: if we draw repeated samples from a population, under the same conditions, and compute 95% confidence intervals for the slope and intercept, 95% of these intervals should include the unknown population values for the slope and intercept. Of course, since the true population values are not known, it is not possible to tell whether any particular interval contains the population values. Quite often, neither the confidence interval for the slope nor the one for the intercept contains the value zero. An interval will only include zero if you cannot reject the null hypothesis that the slope or intercept is zero, at an observed significance level of .05 or less.




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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