Linear regression

[#1]

Hi, 

I am looking for the correct term for what I am using to analyze my data, to my understanding it's neither multiple nor multivariate linear regression:

I want a global linear fit for several measured specimen. So I measured x and y for 5 samples, each yielding y=mx+n. I perform a linear regression of all these 5 samples at once, yielding one m and n for all 5. What's the name for this? In JMP I use "fit model" with role variable y, model effect x and then cross with the specimen number.

Thank you, I couldn't find this in my search so far!

[#2]

I assume that by "several measured specimen" you have 5 observations of (x,y). You use simple linear regression to fit the linear trend model, y = mx + n. You fit such a model with either Bivariate (through Fit Y by X command) or Fit Least Squares (through Fit Model command).

[#3]

Hi,

Thank you for your reply! Enclosed is an example report. I am not sure that the Fit model command actually does what I hope it does:

There are 5 different chips with linear dependencies, they should have the same slope but different intercepts. I would like to obtain one single slope which fits best for all 5 chips. I think this is what is given as estimate for temperature (the independent variable)? I am not sure what the estimates for every single chip represent and why there are only 4 instead of 5.

[#4 · Accepted solution]

There are only 4 coefficients for the 5 crossed effects because one must be left out (as it is determined by the other 4).  If you want to see the 5 coefficients, click on the red arrow and get the Expanded Estimates to see all 5 levels.  Also, if you believe there to be a common slope (as the graph suggests), then I wouldn't include the cross term.  Just include the chip variable and you will get the estimated intercepts for each chip and only one common slope estimate.

[#5]

Thank you! Yes, the cross term was not what I was looking for. So with just adding the chip as model effect the evaluation would still be considered a simple linear regression?

[#6]

No. A simple linear regression would be the result if you fit a line to the data separately for each level of Chip. You can easily do that in Bivariate if you put Chip in the By analysis role or if you use the Group By menu command in Bivariate. The SLR results, though, are independent. The intercept and slope are not related across the chips. You want to constrain the slope of all chips to be the same, so you use a multiple regression model in which you can add terms to represent how you think the response is related to the predictor variables.

[#7]

Thanks so much for clearing that up!

[#8]

I'm coming in late but I found out the Parallelism test in Nonlinear fits also yields a common slope as desired.
In the Analyze menu tab, select Specialised modelling and select Nonlinear. Group your data (in your case, by chips) in the dialog box and Run model. In the Fit window, select Polynomials (Linear fit) under the Fit Curve tab (red triangle). This by default yields independent slopes and intercepts for all the groups. To share the slope, select Test Parallellism in the Linear Fit Tab (red triangle). A new tab opens with the Parallel Fit Parameter Estimates where you will find the shared slope and individual intercepts. I hope this helps.