# question about multiple regression with categorical predictors

I would need a little clarification on this very basic issue. I'm trying to predict a continuous outcome based on a continuous predictor and a categorical variable with 3 levels using multiple linear regression. The fit tells me that when the continuous variable increases, also my dependent variable increases. Fair enough. On the other hand, it is also telling me that being in either of the k-1 categories decreases my dependent variable with respect to the baseline. If I check the mean value of the dependent variable in the three categories, nevertheless, I notice that, as a matter of fact it is higher in the two categories with respect to the baseline. What do I conclude from this? It sounds a little counter intuitive to me..

You fit 3 straight lines with the same slop and 3 different intercepts in the analysis. Let $$\hat{Y_1} = \hat\beta_{01} +\hat\beta_1 X \text{ for reference}$$ $$\hat{Y_2} = \hat\beta_{02} +\hat\beta_1 X$$ $$\hat{Y_3} = \hat\beta_{03} +\hat\beta_1 X$$ "being in either of the k-1 categories decreases my dependent variable with respect to the baseline" means $\hat\beta_{02}$ and $\hat\beta_{03}$ < $\hat\beta_{01}$.
"If I check the mean value of the dependent variable in the three categories, nevertheless, I notice that, as a matter of fact it is higher in the two categories with respect to the baseline." means $\bar{Y_1} < \bar {Y_2}$ and $\bar{Y_3}$, where $$\bar{Y_1} = \hat\beta_{01} +\hat\beta_1 \bar{X_1} \text{ for reference}$$ $$\bar{Y_2} = \hat\beta_{02} +\hat\beta_1 \bar{X_2}$$ $$\bar{Y_3} = \hat\beta_{03} +\hat\beta_1 \bar{X_3}$$
So although $\hat\beta_{02}$ and $\hat\beta_{03}$ < $\hat\beta_{01}$, given $\bar {X_1} < \bar {X_2}$ and $\bar{X_3}$ and the differences are large enough, you will get that $\bar{Y_1} < \bar {Y_2}$ and $\bar{Y_3}$ because $\beta_1 > 0$ as you noticed. So checking $\bar {X_1}, \bar {X_2}, \bar{X_3}$, you will find the answer.
($\bar X$ means the sample mean.)