What are the limitations of linear regressions?

It is limited to Linear Relationships. Through its nature, linear regression only looks at linear relationships among dependent & independent variables.

Linear Regression Only Looks at the Mean of the Dependent Variable. For example, if you look at the relationship between the birth weight of infants and maternal characteristics such as age, linear regression will look at the average weight of babies born to mothers of different ages.

Linear Regression is very sensitive to Outliers. Outliers could have huge effects on the regression. We could deal with this problem by requesting influence statistics from our statistical software

Data should Be Independent. Which means that the scores of one subject (such as a person) have nothing to do with those of others. This is often, but not always, sensible. Two common cases where it does not make sense were clustering in space and time.