linear fit with fitlm or regress

Hi

I have a data set of three variables. I want to use the equation y = a + b*temp + c*temp* sigma. When i write this like y~temp+(sigma*temp) in fitlm, I get 4 terms, Intercept, temp, sigma and temp:sigma.

My question is if sigma is the slope c and temp:sigma is temp*sigma for the c? I think this is correct, but I have not been able to figure out how the equation would look like based on the input arguments. The displayed "Linear regression model" is y ~1 + t*sigma

Thanks a lot!

Answer 1

[Jeff Miller]

Your three variables are y, temp, and sigma? If I understand the model you want to fit, you might get a cleaner picture if you form a new variable:

prod = temp.*sigma;

and then use

y~temp+prod

[Andreas Grøvan Aspaas]

Thanks, but it does not do the trick. As I do not know how to do it I might have explained it poorly.

I try to get y = (a0+b0*T) + (c0*sigma+d0*T). What I suspect is that d0*T is insignificant, but I need to prove it and so far I am only able to get a0,b0 and c0. I do not know how to get a separate d0*T for the slope. sigma should not have anything to do with a0.

[Jeff Miller]

I don't understand why there are two T terms in your model

y = (a0+b0*T) + (c0*sigma+d0*T)

The parentheses don't matter for addition, so your model is the same as

y = a0+b0*T +d0*T + c0*sigma, or

y = a0 + (b0+d0)*T + c0*sigma

In the end I see only one multiplier of T, (b0+d0), not two.

[Andreas Grøvan Aspaas]

Okay. So if prod = t*sigma, and i use y~t+prod I get a0, b0 and c0. Is that c0 the same as c0 and d0 combined?

If I use y~t+sigma*t, I get a0,b0,c0,d0, where the d0 is t:sigma, but I guess that t:sigma is the same as the prod which is uncorrect as I want the T dependence of the slope.

[Jeff Miller]

Sorry, I just don't understand what model you are trying to fit. You say you are trying to get

y = (a0+b0*T) + (c0*sigma+d0*T)

but that does not look like a legitimate model to me as I said before.

[Andreas Grøvan Aspaas]

Ok. It might not work. I was just thinking that I should be able to make whatever formula I wanted if I told matlab to make it.

I think the prod method you proposed works though. I do not get c0 and d0, but I get them both combined if I am not wrong. And this is enough as I just need to know how significant it is. It would be better to have them separated, but as I am not able to I am going to just accept it.

Thanks a lot for taking the time!