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Econometrics: Ordinary least squares estimation · The Least Squares Principle

Why OLS minimizes squared residuals, what that guarantees about the fitted line, and how to read and rescale its estimates.

Econometrics · 28 questions

Try 3 questions

1. Ordinary least squares (OLS) picks the intercept and slope that minimize what?

  1. The sum of squared residuals
  2. The largest single residual
  3. The sum of absolute residuals
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Answer: The sum of squared residuals

That is the definition of least squares: among all lines, OLS chooses the one whose squared vertical misses, added up, are smallest.

2. In a fitted regression, what is a residual?

  1. The fitted y minus the mean of y
  2. The true error term in the population
  3. The observed y minus the fitted y
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Answer: The observed y minus the fitted y

A residual is the sample miss, y minus ŷ. The population error is unobservable; residuals are only its estimates.

3. Why can't a regression method simply minimize the plain sum of the residuals?

  1. Plain sums ignore how many points there are
  2. Positive and negative misses would cancel out
  3. The sum is always too large to minimize
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Answer: Positive and negative misses would cancel out

Any line through the means makes raw residuals sum to zero, however badly it fits. Squaring makes every miss count as a cost.

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