The Method of Least Squares and Simple Linear Regression

THE METHOD OF LEAST SQUARES AND SIMPLE LINEAR REGRESSION 

The Concept of Ordinary Least Squares Applied to the Simple Linear Model 

At the minimum of a function, the first derivative equals zero. In the case of the simple linear regression (SLR) model, Y = 0O + 0i + s, where the function being minimized is the residual sum of squares [Eq. (2.7)], the following equalities must hold 

Intuitively, the concept of least squares makes sense since the predicted model attempts to minimize the squared deviations from the observed values (Fig. 2.1). Under OLS assumptions, every data point contributes equally to the estimate of the slope and intercept. 

The variance of the parameter estimates may then be obtained using the linear expectation rule 

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