Questions / Quant research, Regression & linear algebra
Reverse the regression
For population linear regressions with intercepts, Var(X)=4, Var(Y)=9, and Cov(X,Y)=3. What is the slope when regressing Y on X?
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Answer: 0.75 slope (3/4)
- For regression of Y on X with an intercept, the slope is Cov(X,Y)/Var(X).
- Use X as the predictor: 3/4 = 0.75.
- The variance of Y affects correlation and fit diagnostics, but is not the denominator of this slope.
Interview shortcut. Slope of Y on X is Cov/Var(X) = 3/4.
Takeaway. Name the predictor before choosing the denominator.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.