What are the main assumptions of linear regression?
Linearity between features and target, independent errors, constant error variance (homoscedasticity), roughly normal errors (needed mainly for confidence intervals), and no severe multicollinearity among features.
Explain it simply
Linear regression draws the best straight line (or flat plane) through data. It is only trustworthy when the data behaves roughly like a line plus random noise.
A handy memory aid is LINE: Linearity, Independence, Normality, Equal variance.
Example
Linearity : the true relation is a straight line, not a curve
(area vs price: yes. Age vs height from 0-60: no)
Independence : one row's error does not predict the next
(broken in time series: today's error resembles yesterday's)
Equal variance : spread of errors is the same at all predictions
(broken when big flats have much larger errors than small ones)
Normal errors : residuals look bell-shaped, matters for p-values and intervals
No multicollinearity : features are not near copies of each otherHow to check: plot residuals against predicted values. A curve means non-linearity, a fan shape means unequal variance. A Q-Q plot checks normality. The Durbin-Watson test checks for correlated errors.
Predictions can still be useful when assumptions are mildly broken, but the coefficients' standard errors and p-values become unreliable.
What to say in the interview
"The assumptions are linearity, independent errors, constant variance, normally distributed residuals and no strong multicollinearity. I check them with residual plots, a Q-Q plot, Durbin-Watson and VIF. Violations hurt inference more than raw prediction accuracy."
Common mistakes
- Saying the features themselves must be normally distributed; the assumption is about residuals.
- Ignoring residual plots and trusting R squared alone.