- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 1. Linear regression

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**CFA Practice Question**

A regression based on 15 observations was estimated as given below:

R

_{Stock}= 0.0005 + 0.98 R_{Index}Based on the regression results, a 1% change in the index return will result in,

A. 1.03% change in the stock return.

B. 9.8% change in the stock return.

C. 0.98% change in the stock return.

**Explanation:**The co-efficient of the dependent variable determines the sensitivity of the dependent variable to the independent variable. In this case, if the return on the index changes by 1%, the return on the stock would change by 0.98% (= 0.98 x 1%).

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**User Contributed Comments**
5

User |
Comment |
---|---|

eddeb |
Don't get caught with the linear regression. Its the co-efficient that dertermines the sensitivity of the dependent variable |

steved333 |
y=mx+b, baby! .98 is m! (gotta love pre-algebra) |

Paulvw |
Careful with this one! While the intention is clear, the question has no answer. If for example, the return on the index is .0001 before changing, a 1% change in the index will change the stock return from 0.000598 to 0.000599, a 0.16% change, not a 0.98% change. |

ricardo152 |
Paulvw: your calculation is wrong due to rounding. Go with the formula, not specific numbers. |

endurance |
Read carefully. The question ask for the change, not the return. So, we have to look at the response (b1) to changes in the independent, i.e. how will stock return change, when index changes. (0.98x.0.01) = 0.0098 => 0.98 percent |