Statistics for finance · level 2
Regression slope and R²
A simple regression is correlation in disguise. The slope is ρ scaled by the ratio of the spreads, and R² is just ρ squared.
Worked example: Simple regression with correlation ρ = 0.6. What is R², in %?
ρ0.6
R²36%
Step by step
- 1
In a one-variable regression R² = ρ²
0.6² = 0.36
- 2
As a percentage
36% of the variance in y is explained by x
Simple regression with correlation ρ = 0.6. What is R², in %? = 36
The theory behind it
Intuition
A regression slope is correlation scaled by the ratio of spreads, and R² is simply r² — the share of variation explained.
Common pitfalls
- ×Interpreting the intercept outside the data range.
- ×Reading a high R² as a valid model when residuals are patterned.
In the interview
Reading a regression output exhibit and saying what it means.