# parameter estimate of categorical variable

#### szm

##### Member
I run multiple regression with 2 continuous and 1 categorical variable (3 levels).
SAS will hold the last level of the categorical variable and will not give an estimate. I know that this is the intercept.
My question is how to calculate the interaction of the continuous variable with the 3rd level of the categorical variable that I don't get an estimate?

PHP:
Effect	increment	Estimate	Standard Error
Intercept		     10.8879	51.1246
x		             0.003093	0.0658
y		             -0.3009	2.0023
increment	one	65.6866	12.3805
increment	two	-30.1428	12.3987
increment	three	0       	.
x*increment	one	-0.09041	0.01706
x*increment	two	0.0387	0.01709
x*increment	three	0       	.
Thank you.

#### Dason

Your question doesn't quite make sense. The estimate of the slope (x) IS the estimate for the third level.

#### szm

##### Member
Thank you for answering a question that you didn't quite understand!

Last edited:

#### Dason

Thank you for misinterpreting my response by assuming that I'm the idiot!

It's not that *I* didn't understand your question - it's that your question doesn't make sense. It's like if somebody asked "How do I add this apple to 7?"

The model you fit doesn't give you an interaction term for the third category because that doesn't make sense in your model - it just directly gives you the slope for the third category (and that slope is the estimate listed under x). You have estimates for interaction for the other two categories because those ask the questions "Is the slope for category 2 different than the slope for category 3 (which is used as the reference level)" and "Is the slope for category 1 different than the slope for category 3". It doesn't make sense to ask the question "Is the slope for category 3 different than the slope for category 3".

If you care to elaborate on what you're actually interested in then maybe we can help. Or maybe I'm an idiot and won't understand your questions...

#### trinker

##### ggplot2orBust
Dason said:
How do I add this apple to 7?"
Actually this is quite easy. Check my work below:

$$\sum_{k}^{i =1}\alpha \therefore \Re \varnothing \P \left ( {7_{x}}^{y} \right )\rightarrow \frac{x_{y}^{z}\textrm{apple}}{\pi ^{apple}}$$

#### BGM

##### TS Contributor
Actually this is quite easy. Check my work below:

$$\sum_{k}^{i =1}\alpha \therefore \Re \varnothing \P \left ( {7_{x}}^{y} \right )\rightarrow \frac{x_{y}^{z}\textrm{apple}}{\pi ^{apple}}$$
Wow I never know adding this apple to 7 is so easy. Thanks trinker.

#### szm

##### Member
Dason,

I did not call you or insinuate that you are an idiot... Actually I thanked you for answering my question.
Was it my lack of stat knowledge..? My bad English..? Or am I just an idiot that cannot form a question that makes sense..?
Maybe you meant that I am a little bit of all the above..

Your second reply (most of it except the first and last sentence) was the explanation that really helped me to understand what I was missing.

I guess it is nice to have you on this forum helping people like me because it seems that you have a solid knowledge in stats.
However, the vague part of your first reply did not help at all and made me think that you are just being sarcastic..

#### trinker

##### ggplot2orBust
@szm Keep in mind all we have here is our writing, so typical social cues and context are absent. Before jumping to conclusions please assume the best intentions of others and ask for clarification if you believe someone has/is being rude.

Dason's style is to try to ask the right questions that make you examine your own problem. It's very effective.

#### szm

##### Member
I understand that and maybe I should just say thank you and nothing else. But no effective question was asked...
Anyway, I just thanked him in a joking manner. I wasn't trying to create an issue.

#### noetsi

##### Fortran must die
Maybe we should just stick to the technical details and not personal comments. I am going to delete the personal comments from this thread in the future. If they continue to much further I am going to close the thread reluctant as I am to do that.

Curtesy goes a long way.