Econometrics · intermediate
What moves on the Linear Regression & OLS diagram
When an omitted variable correlates with both X and Y, OLS loads its effect onto X. Controlling for it removes the borrowed slope: omitted variable bias, corrected.
The raw fitted line looks steep: X seems to matter a lot for Y.
But part of that slope belongs to a lurking third variable correlated with both.
Adding the control, the line tilts flatter around the middle of the data.
The original slope was biased upward: omitted variable bias in action. Which line is 'true' depends on what question you are asking.
Examiners ask this as: omitted variable bias, ability bias, add a control, confounder, slope shrinks.
Other scenarios on Linear Regression & OLS