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I learnt linear regression before I was introduced to ANOVA/ANCOVA. It helped my understanding to think of one-way ANOVA and ANCOVA using analogies in linear regression.

Can you help me understand how two-way ANOVA and factorial ANOVA are difference from each other and from ANCOVA using linear regression analogies (if there are any)?

Do these ANOVA-based techniques offer anything additional to linear regression?

EDIT: may be a better way to phrase it is in relation to linear regression

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  • $\begingroup$ "It helped my understanding to think of one-way ANOVA and ANCOVA using analogies in linear regression." -- So how do you understand this analogy? $\endgroup$ – amoeba Apr 23 '18 at 10:59
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    $\begingroup$ I don't know why your question was downvoted; +1 from me. $\endgroup$ – amoeba Apr 23 '18 at 12:14
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Compared to one way ANOVA:

Two way ANOVA adds one more categorical independent variable to the regression (and possibly the interaction between the two IVs).

Factorial ANOVA adds any number of categorical IVs to the regression (and maybe some interactions among them).

ANCOVA adds a continuous variable to the regression (and maybe some interactions).

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