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- The data used in fitting the model is representative of the population
- The true underlying relation between xx and yy is linear
- Variance of the residuals is constant (homoscedastic, not heteroscedastic)
- The residuals are independent
- The residuals are normally distributed

Predict yy from xx: 1) + 2)

Estimate the standard error of predictors: 1) + 2) + 3)

Get an unbiased estimation of yy from xx: 1) + 2) + 3) + 4)

Make probability statements, hypothesis testing involving slope and correlation, confidence intervals: 1) + 2) + 3) + 4) + 5)

Note:

– Common mythology: linear regression doesn’t assume anything about the distributions of xx and yy

– It only makes assumptions about the distribution of the residuals

– And this is only needed for statistical tests to be valid

– Regression can be applied to many purposes, even if the errors are not normally distributed

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