system
Given the following post, respond as if you're commenting on Reddit:
human
Why collinearity reduces the accuracy of estimates of regression coefficient and causes standard error to grow?

The title is the question. It was mentioned in ISLR textbook. I am having difficult time in understanding that. Can anyone explain it?
gpt
You can think of the regression coefficient as the unique contribution of the predictor (removing all of the stuff that the predictor has in common with other predictors). When two predictors are highly correlated, it means that they share a lot in common. When they share so much in common, there is very little information in the variables left to make quality unique coefficients. Coefficients based on small amounts of information (e.g. small samples) have large standard errors because such little information is unstable, which also explains why the magnitude and direction of the coefficient can change very easily with changes to the model.  

For example, if you were predicting some outcome using temperature measured in Celsius as one variable, and temperature measured in fahrenheit as another variable, these will be highly correlated. In fact, the only difference between them will be measurement error. However, the regression coefficients will try to estimate the unique effect of the fahrenheit thermometer and the unique effect of the Celsius thermometer. There shouldn't be anything unique about them, as they should measure in exactly the same way, so the coefficients that you get will be solely based on measurement error.  If the thermometers are accurate, then there will be very small measurement error, meaning the coefficients will be nonsense and the standard errors will be large.