Principles of Finance · free preview
Linear Regression and the Best-Fit Line
Linear regression fits a line through a scatter by minimizing the squared vertical distances, producing a slope and intercept that predict the dependent variable from the independent one, under assumptions whose violation limits the fit's trustworthiness.
1. The regression line
The regression line
2. Least squares, the fitting principle
Least squares, the fitting principle
3. A worked miniature
A worked miniature
4. The assumptions and their audit
The assumptions and their audit
5. The regression's purpose
What does a linear regression of y on x produce?
6. The least squares rule
According to the least squares principle, which line is chosen as the best fit?
7. The slope's formula
In a regression, the slope equals the correlation multiplied by what ratio?
8. Reading the advertising slope
A regression of sales on advertising returns a slope of 4.5. What does that number mean in practice?
9. The residual's role
What does a residual represent in a regression?
10. The extrapolation warning
Why is predicting sales at double the highest observed advertising level dangerous?
11. The fitting principle's name
What two-word term names the rule that chooses the line minimizing squared residuals? Answer in lowercase.
12. The dependent variable's axis
In the regression line y equals a plus bx, which variable is being predicted? Answer with one letter.
13. The slope-correlation link
The slope equals the correlation times the ratio of which two standard deviations, numerator first? Answer with two letters separated by a space.
14. The report card plot
What two-word term names the diagnostic plot of residuals against fitted values used to audit regression assumptions? Answer in lowercase.
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