Use the original fitted equation
The original line is fitted asset return=1.2%+2.1×benchmark return. SSE=1.2 and Syy=45.3 in percentage points squared, with five observations.
Retain the descriptive task
The questions calculate supplied fitting quantities. No significance test, future-return probability or official question source is implied.
Try the questions
At benchmark 1% and observed asset 2.5%, what is the residual?
- A.
−0.8 percentage points
- B.
+0.8 percentage points
- C.
1.5 percentage points
Answer and explanation
Answer: A
A residual subtracts the fitted line, not a unit benchmark return.
- A
Fitted return is 3.3%, and observed minus fitted is −0.8.
- B
This reverses the defined residual sign.
- C
This is asset minus benchmark, not the fitted residual.
What is the residual standard-error calculation?
- A.
√(1.2/3)
- B.
√(1.2/4)
- C.
1.2/3
Answer and explanation
Answer: A
Take the square root after the appropriate squared-sum division.
- A
Two fitted coefficients leave n−2=3 residual degrees of freedom.
- B
This is sample dispersion of these residuals, a different divisor.
- C
This remains on the squared-return scale.
If asset returns are constant and the benchmark varies, what does this tool report?
- A.
Slope zero and a defined intercept; correlation/R² omitted as undefined
- B.
R² 100% by definition
- C.
No intercept can be estimated
Answer and explanation
Answer: A
A constant fit and a defined variation ratio are different questions.
- A
The response dispersion denominators vanish.
- B
That invents an explained-variation ratio at 0/0.
- C
The varying benchmark still identifies the straight line.