Essentially,the relations that are tested through ANOVA could also be tested through regression analysis (by dummy variables).

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This is true. In fact, ANOVA can be thought of as a special case of regression analysis when there is only one categorical variable (i.e. no interaction terms or continuous predictors). The use of dummy variables in regression allows us to test the specific effects of each group in a categorical variable, just as ANOVA does.

Essentially,the Relations That Are Tested Through ANOVA Could Also Be