Linear regression models and BLUE

Regression estimates how a dependent variable moves with explanatory variables. The simple model is Y = a + bX + u, where u is the error term capturing everything else. Ordinary least squares (OLS) chooses a and b to minimise the sum of squared residuals — the vertical gaps between actual and fitted values. Worked example: if the estimated line is Y = 10 + 2X, then a one-unit rise in X is associated with a 2-unit rise in Y, and at X = 5 the predicted Y is 20.