Confidence Intervals from multiple regression

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Stephen Conley
Stephen Conley 2011-4-21
I am using the regress function in the statistics toolbox to estimate how the ozone concentration (near Christmas Island) varies in time and space. The function returns the coefficients (which seem reasonable) along with confidence intervals for the coefficients (which seem really small). For example, the coefficient for time is returned as -0.31 ppb/hour (totally reasonable) but the 95% confidence interval for it is (-.318, -.307) which seems really tight given the R2 value for the entire fit is only 0.55. Is it conceivable that the R2 could be that low with a confidence interval that tight?

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回答（1 个）

Tom Lane
Tom Lane 2011-5-5
This is conceivable. If you have lots of data, you might be able to estimate the coefficients very accurately even though there is lots of residual variation so your R^2 value is not close to 1.

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