What does the method of least squares do?

What does the method of least squares do?

• A. A method of estimating parameters by maximizing the likelihood.
• B. A method of estimating parameters by minimizing absolute errors.
• C. A method of estimating parameters by minimizing the sum of squared errors.
• D. A method of estimating parameters by resampling.

Answer: (C)

The method of least squares estimates parameters by minimizing the sum of squared differences between the observed values and the model’s predicted values. In regression, this means choosing the parameter values that make the residuals (the gaps between what we observe and what the model predicts) as small as possible when their deviations are squared and summed over all data points. Squaring the residuals punishes larger errors more and leads to a solvable optimization problem, giving a concrete, often unique solution under typical conditions. Under Gaussian error assumptions, these least-squares estimates also align with maximum likelihood estimates, but the defining idea remains minimizing the total squared error. It’s not about maximizing likelihood, nor about minimizing absolute errors (that would be a least absolute deviations method), nor about resampling techniques like bootstrapping.

The method of least squares estimates parameters by minimizing the sum of squared differences between the observed values and the model’s predicted values. In regression, this means choosing the parameter values that make the residuals (the gaps between what we observe and what the model predicts) as small as possible when their deviations are squared and summed over all data points. Squaring the residuals punishes larger errors more and leads to a solvable optimization problem, giving a concrete, often unique solution under typical conditions. Under Gaussian error assumptions, these least-squares estimates also align with maximum likelihood estimates, but the defining idea remains minimizing the total squared error. It’s not about maximizing likelihood, nor about minimizing absolute errors (that would be a least absolute deviations method), nor about resampling techniques like bootstrapping.