# Difference between linear model and linear regression

I am interested in the difference between a linear regression and a linear model. In my understanding, linear regression is part of a larger family of linear models but both terms are often used as synonyms. Now, it has been suggested to me, that I could replace a regression analysis by a linear model to bypass the assumptions that need to be met when performing linear regression. If you have any reading suggestions on the topic, they are very welcome.

I would like you to help me figure out whether what I do

• is linear regression, and should be treated like it
• could be replaced by a "linear model"
• my method is synonym to a "linear model"

So, here is what I did for short. The purpose of the analysis was to plot a line in a scatter plot. Both slope and intersection point of the line with the x-axis would be used to analyze the dataset. The outcome variable was a rate (concentration per time) of a chemical element and the predictor was a ratio of two concentrations (so no unit). I measured rates in different environments (depths), which have to be compared in one plot. Only one of the depths does not fit regression assumptions.

1. I used the lm function in R to calculate a linear equation.
2. I checked the residuals of the lm object.
3. I found that residuals were neither normally distributed nor had equal variances.
4. I figured that log-transformation of the outcome varibale (rate) would fix the variance, but residuals were still not normally distributed.
5. I decided on using a robust method so the equation would be less biased by outliers, which I cannot exclude from analysis (function lmrob, package robustbase).
6. I did not plot the line because of the log-transformation. There is other data in the plot that does not need to be log transformed, but should stay comparable to the dataset causing trouble. It is also not possible to expand the plot by another one with a log-scale, because the original plot is part of a multiple plot design, that is already quite extensive.

Maybe for my purpose the regression assumptions are not of interest? Right now, I am rather stuck about what to do, so thank you for your help!

• A related question here. – Richard Hardy Mar 16 '16 at 11:37
• Could you say a bit more about your problem at hand: the nature of the data (in particular, are any necessarily positive); whether the log transformation was done on predictors or the outcome variable; why you could not "plot the line because of the log-transformation." – EdM Mar 16 '16 at 13:17
• @Richard Hardy: Thank you for the comment, but I am still not sure about what to do in my case. – Syrafina Mar 17 '16 at 7:13
• @EdM: I tried to be a bit more specific and edited my question. I did not add to much detail because I think my problem is more a general one. Hopefully, the edit is a help for comments on the question. – Syrafina Mar 17 '16 at 7:19
• @Syrafina, I do not know the answer to your question; my comment just pointed to a somewhat related thread, that's it. – Richard Hardy Mar 17 '16 at 7:55