Why do we need the LINE assumptions?

So far, you have implemented two approaches for performing inference assessment to a linear model. The first way is given by the standard R output (lm) and is based on the t-distribution. The derivation of the t-distribution is based on the theory (i.e., the LINE conditions).

The second method uses a randomization test which assumes that the observations are exchangeable under the null hypothesis. That is, when the null hypothesis (X is independent of Y) is true, the Y values can be swapped among the X values. The technical conditions in the randomization setting are linear relationship, independent observations, and equal variances. However, the normality assumption is not needed.

What happens if inferences is performed when the technical conditions are violated?

Possible Answers

If the technical conditions are violated, the software will not compute a p-value.
If the technical conditions are violated, the p-value will not represent the probability of the data given the null hypothesis is true.
If the technical conditions are violated, the CI procedure will not capture the true parameter in 95% of samples.
All of the above.
Some of the above.

Exercise

Why do we need the LINE assumptions?

Instructions

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