- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 2. Testing the Significance of a Regression Coefficient

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**CFA Practice Question**

Suppose you want to know whether Fidelity Select Technology Fund (FSTF) behaves more like a large-cap growth fund or a large-cap value fund. You want to estimate the regression Y-hat

_{t}= b_{0}+ b_{1}X_{1t}+ b_{2}X_{2t}+ e_{t}, where Y_{t}is the monthly return to the FSTF, X_{1t}is the monthly return to the S&P 500 Growth Index, and X_{2t}is the monthly return to the S&P 500 Value index. The table below shows the results of a multiple linear regression using monthly data from December 1994 through March 2009.

Use a 5% significance level and determine whether changes in the monthly return to the S&P 500 Value index affect FSTF's returns.

Correct Answer: The null hypothesis is H

_{0}: b_{2}= 0, and the alternative hypothesis is H_{1}: b_{2}≠ 0. The t-statistic is (-0.0519 - 0)/0.2052 = -0.2529. The t-test has 172 - 2 - 1 = 169 degrees of freedom. The critical value for the test statistic at the 0.025 significance level is about 1.96. As the absolute value of -0.2531 is less than 1.96, we fail to reject the null hypothesis that b2 = 0.###
**User Contributed Comments**
6

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

jhmorris |
Other than simply looking it up in the t-distribution tables, is there a way in which you can determine the critical value from the information given in this problem? |

noonah |
You can determine t-critical only from the tables, and not from the info given above |

BMurphy |
as with level 1, you should memorize the basic t-critical values for certain common confidence levels, 90%, 95%, 99% -- just be careful to always identify whether it is a two-tailed or 1-tailed test. |

scottharris |
Memorize them for every different degree of freedom? Go for it, but I'll gamble on the table being given in the exam thanks. |

xyzanand |
The t-statistic is given in the table above :-) |

pjdeschenes |
For high values of n, the student's t distribution closely resemples the standard normal distribution. 1.96 as the critical value for 2.5% significance is worth memorizing for the standard normal distribution. |