- 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**

Beth has two independent variables and 25 observations in her regression analysis. The t-statistic for one of the independent variables X

_{1}is 1.83. She wants to test H_{0}: β_{1}>= 0 against H_{1}: β_{1}< 0. What is the critical value for Student's t distribution and is the variable significant at the 5% confidence level?

A. The critical value is 1.714, and the variable is significant.

B. The critical value is 1.717, and the variable is significant.

C. The critical value is -1.717 and the variable is not significant.

**Explanation:**Note that H

_{1}is β

_{1}< 0!

The degrees of freedom: 25 - 2 - 1 = 22.

Critical value -t

_{0.05, 22}: -1.717.

As -1.717 < 1.83, the variable is NOT significant at the 5% confidence level.

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**User Contributed Comments**
6

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

tumanta |
I did not get the reason why critical t value is negative. Can anybody throw some light? |

Reinhard2 |
You want to prove that beta is smaller than 0. This means it has to be at least negative and enough away from zero. Basically smaller than -1.717. |

NetteBrd |
We are testing that Beta is >=0 Beta <0 is the alternative H so it should be significant... or not? And it should be a critical value of 1,714 because the T-Statistic has 2degrees of freedom or not? |

r3n1 |
Reinhard2 thanks for the posting. |

StJohnDale |
One tailed = or not =; Two tailed above or below (ie < or >) H0: B1>= 0 - therefore we are looking at one tailed test. We are trying to reject H0 to prove that B1 is less than zero ie H1. Therefore we are in the lower tail not the upper tail. Because we are in the lower tail the critical t is negative. ie -1.717. DF = n-k-1 = 25-2-1 =22 |

StJohnDale |
Critical t = -1.717 < Calc t = +1.83. Therefore we fail to reject H0. Therefore variable is not significant. I think thats right? |