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Analysis of Covariance. This is really a special case of multiple linear regression, used in ANOVA-like settings with some continuous covariates in addition to the categorical ones.

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Slope is negative but confidence limits contain zero, how do I describe the effect?

Confidence limits are not hard limits but randomly vary with the data. With a method that generates confidence limits that cover an unknown constant with some probability, you can make a reasonable as …
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