I read the following (Wikipedia) regarding contrast coding of categorical variables:

Unlike when used in ANOVA, where it is at the researcher’s discretion whether they choose coefficient values that are either orthogonal or non-orthogonal, in regression, it is essential that the coefficient values assigned in contrast coding be orthogonal.

What is the precise notion of orthogonality used here? Why is this important and why is it "essential" that in regression the coefficient values are orthogonal?


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