Econometrics: Why More Police Can Mean More Crime
The tools economists use to turn messy data into evidence, from least squares and p-values to instruments, panels and random walks, and the traps that fool them.
Try 3 questions
1. Ordinary least squares picks the regression line that minimizes what?
- The sum of squared residuals
- The number of outlying points
- The sum of absolute residuals
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Answer: The sum of squared residuals
OLS squares each vertical gap between data and line and adds them up; squaring penalizes big misses heavily and gives a neat formula.
2. In a regression of the log of wages on years of schooling, the slope is 0.08. What does that roughly mean?
- Each extra year adds 0.08 units of money
- Each extra year links to about 8% higher pay
- Schooling explains 8% of wage differences
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Answer: Each extra year links to about 8% higher pay
With a logged outcome, a slope of 0.08 means one more unit of x is associated with roughly an 8 percent change in y.
3. What is always true of OLS residuals when the regression includes an intercept?
- They sum exactly to zero
- They follow a normal distribution
- They are all positive in large samples
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Answer: They sum exactly to zero
Including a constant forces the fitted line through the means of the data, which makes the residuals add up to zero by construction.
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