Principles of Finance · free preview
Predictions and Prediction Intervals
A regression point prediction inherits uncertainty from the line's estimation and the scatter around it, and prediction intervals quantify that uncertainty, widening away from the data's center to give honest ranges for forecasts.
1. From line to forecast
From line to forecast
2. The interval's behavior
The interval's behavior
3. Worked reading
Worked reading
4. Honest forecasting as the course's close
Honest forecasting as the course's close
5. The point forecast's limits
Why is a regression's point forecast, the fitted value at a chosen x, not enough for decision making?
6. The two uncertainties inside a prediction
Which two sources of uncertainty does a prediction interval combine?
7. Why intervals widen at the edges
Why is the prediction interval narrowest near the mean of x and widest at the extremes?
8. Confidence versus prediction interval
What distinguishes a confidence interval for the regression line from a prediction interval for an individual outcome?
9. Reading the funnel
A prediction interval for sales at average advertising runs 40 to 55 units, and at double average spending runs 30 to 70. What does the comparison tell management?
10. Beta's interval and the hedge
A stock's estimated beta is 1.2 with a prediction-style interval from 1.05 to 1.35. Why does this matter for a portfolio manager hedging market exposure?
11. The flaring shape's name
What one-word term, also a laboratory cone, names the shape of prediction intervals around a regression line? Answer in lowercase.
12. The narrow interval's target
What two-word phrase names the quantity a confidence interval prices, in contrast to the individual outcome the prediction interval prices? Answer in lowercase.
13. The scatter's surrogate
What one-word term names the typical residual size, the standard deviation of the scatter around the line, that drives interval width? Answer in lowercase.
14. The substitution forecast
What two-word term names the fitted value y-hat obtained by plugging an x into the estimated line? Answer in lowercase.
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