# In a multiple linear regression how to know when to drop variables?

If I given a model with 3 variables($X_1, X_2$ and $X_3$) and a correlation between them are not high. The highest correlation coefficient from the correlation matrix is equal to $0.699614004$ and is between $X_2$ and $X_3$. Is this coefficient high enough that to drop the variable $X_2$ in order for the model to be precise?

Generally how to know when to drop a variable form the model?

• This is too abstract and over summarized to answer. What are these variables, and what do they measure? What are your goals with the model? Mar 29 '18 at 16:45
• It is a model where Y is performance IQ, and $X_1, X_2,X_3$ are the Brain weight, height and weight of the person. I am asked to determine whether any variables have to be dropped basing on the correlation matrix and the adjusted $R^2$ coefficient , which is $0.2$. Since it is not high I assume I need to drop some variables, however, their correlation coefficients are not very high(the highest one is $0.6996$ and $0.588$). How can I determine which variables should I drop?
– user200918
Mar 29 '18 at 17:04
• Why drop any? Why are you fitting a model? Mar 29 '18 at 17:09
• What Scortchi said. Is the intent of the model to learn about the effect of one of the predictors, to make predictions, something else? Mar 29 '18 at 18:09

Generally speaking, $R^2$ always increases as you increase the number of variables in your model, so by itself it is not a good criterion to know when you should stop adding variables. Instead you should use a different number that in some sense measures that "higher $R^2$ is better, but you don't want too many variables either". Quantities that measure this are the adjusted $R^2$, the AIC, and the BIC.