# How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y).

I would like to test whether individuals belonging to another population (patients), one by one individually, are fitting or not the healthy control regression line. I have both Xs and Y values for the new individuals.

I'm not sure about how to proceed: should I test the individual coefficients compared to the ones of the HC regression line, or should I predict the new Y values based on the HC model and test whether these Y values are significantly different from the actual ones?

• How many predictors does the HC model have? Commented May 20, 2019 at 20:37
• @JamesPhillips 4, corresponding to a cognitive ability measure (the same) across 4 timepoints close in time (we're looking for cognitive performance fluctuations, and whether these are different between healthy controls and patients, at the individual level). Commented May 22, 2019 at 14:22

## 1 Answer

I've found the answer to my own question, in case it'll be useful to someone I post it here.

Once the HC regression has been fitted, I estimated a regression line separately for each individual of the other group. I then used a F statistic to test, all together, whether the linear combination of the parameters of the new regressions are statistically different from the HC ones.

This can be done in R with the package car. Ad example, if we want to test whether a patient with coefficients 5.5, -1, -2 and -2 belongs to the HC population, we can use:

linearHypothesis(lm_healthycontrols,  c("(Intercept) = 5.5", "x1 = -1", "x2 = -2", "x3 = -2"))


If the p-value is significant (say p<0.05), the patient is considered as belonging to a different population (patients).