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I'm a junior engineer at a small biotech company and have some (real) data from a fractional factorial DoE (3 factors, 2 levels, 4 test conditions with six replicates each). Currently, we use excel to analyze this data, although I'm more familiar with Matlab and SAS.

I'm trying to do a multiple linear regression with the data in excel, but the results are a little counter intuitive:

enter image description here

The main issue is that theoretically, I was expecting the relationship to mainly be of the form: Response=log(FOP)-log(Cut). Response is the log of a concentration diluted, and the cut is a dilution factor, so it's surprising that the concentration of the undiluted product has no effect on the response. Moreover, the intercept calculated here is very close to the average value of Log(FOP).

I reran the regression with the intercept set to zero and got these results:

enter image description here

Now things look closer to the theoretical expression, with some possibly useful information about the impact of other process variables. The problem is that the p-values seem suspiciously low, and the R-squared suspiciously high. Obviously forcing the intercept to be zero is not great, but is it normal for there to be such a big difference in the fitted coefficients?

Any guidance would be much appreciated.

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My guess is that your original model had a linear dependence among the predictors, so that you couldn't get an estimate for the logFOP coefficient. I don't know if Excel returns any warnings in that type of situation, or just sets the coefficient value to 0.

With respect to forcing the intercept to be 0, see this page for extensive discussion. If you have a theoretical reason for that restriction it can be OK, but if you are interested in deviations from ideal behavior (as you seem to be) it might not be a good idea.

This page goes into detail about how the regression models differ with and without an intercept. Yes, coefficient estimates can differ substantially, as you are fitting 2 fundamentally different models.

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  • $\begingroup$ Thank you, those two links actually go together to explain my issue. The issue is that I can write Const as a linear combination of Log(FOP) and Log(Cut), which I expected. I gather that in this case, it's ok to use RTO or to drop Log(FOP) as predictor variable? $\endgroup$
    – Karsten Skogsholm
    Commented May 14, 2022 at 19:53
  • $\begingroup$ @KarstenSkogsholm I'd say to drop logFOP. I'm uncomfortable with forcing fits through 0, although that can sometimes be OK. Think carefully about which model will best meet your practical needs. $\endgroup$
    – EdM
    Commented May 14, 2022 at 22:19

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