The least-squares objective function sums the squared residuals over all observations. A residual is defined as the observed y value minus the line’s predicted value.
Conditions: The model is simple linear regression.; Residuals are defined as observed y minus predicted y.
The least-squares objective function sums the squared residuals over all observations. A residual is defined as the observed y value minus the line’s predicted value.
Conditions: The model is simple linear regression.; Residuals are defined as observed y minus predicted y.
By setting the partial derivative of the least-squares objective with respect to the intercept to zero, we obtain the relationship: intercept = mean(y) − slope · mean(x). This implies that the fitted line always passes through the point of sample means.
Conditions: The model includes an intercept term.; The derivative is taken with respect to the intercept parameter.
By setting the partial derivative of the least-squares objective with respect to the intercept to zero, we obtain the relationship: intercept = mean(y) − slope · mean(x). This implies that the fitted line always passes through the point of sample means.
Conditions: The model includes an intercept term.; The derivative is taken with respect to the intercept parameter.