In regression with dummy variables,the predicted Ŷ for each category is the mean of Y for each category.

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In regression with dummy variables, the predicted Ŷ for each category is indeed the mean of Y for each category. This is because the dummy variables represent categorical variables and can only take the values of 0 or 1, indicating whether an observation belongs to a particular category or not. Thus, the coefficient of each dummy variable represents the difference in the mean of Y between the category represented by the dummy variable and the reference category (usually the one with the lowest or highest value). Therefore, when predicting Ŷ for a particular category, we simply take the mean of Y for that category, which is the same as the intercept term in the regression model.

In Regression with Dummy Variables,the Predicted Ŷ for Each Category