- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 5. Testing the significance of a regression coefficient

###
**CFA Practice Question**

To help gain a better understanding of the relationship between the return on the common stocks of small companies
and the return on the S&P 500 Index, you run a simple linear regression to quantify this relationship, using the monthly
return on small stocks as the dependent variable and the monthly return on the S & P 500 as the independent variable. The results of the regression are shown below:

Residual Standard Error is 19.85

Correlation coefficient is 0.7740

N=75

F-value = 101.465 on 1,730 degrees of freedom.

The percent of the variation in the return on the dependent variable (return on small stocks) explained by the return on the independent variable (return on the S & P 500 ) for the period under study was:

The t-statistic critical level at the 0.01 level is 2.66

Residual Standard Error is 19.85

Correlation coefficient is 0.7740

N=75

F-value = 101.465 on 1,730 degrees of freedom.

The percent of the variation in the return on the dependent variable (return on small stocks) explained by the return on the independent variable (return on the S & P 500 ) for the period under study was:

A. 10.07 percent.

B. 59.91 percent.

C. 77.40 percent.

**Explanation:**Coefficient of determination = (correlation coefficient)

^{2}

R

^{2}= 0.774

^{2}

=0.5991

###
**User Contributed Comments**
3

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

dimanyc |
I loved that question because this is exactly how they will try to screw you over at the exam - by giving you 100 data points from which you only need to use 1. |

Tomas |
Thats the way to test whether you understand the problem... |

adamrej |
Indeed, all you need is r. On a separate note, I think the F-value given is incorrect. There's a relationship between F-value and R^2: F= R^2/(1-R^2) * (n-k-1)/k and it does not hold here |