- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 7. Analysis of variance (ANOVA)

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**CFA Practice Question**

An analyst is currently reviewing the following regression analysis:

B. Since the calculated t-statistic of 2.88 exceeds the critical t-statistic, the null hypothesis is rejected.

C. Since the calculated t-statistic of 6.88 falls within the critical t-statistic, the null hypothesis is accepted.

At a significance level of 5%, which of the following statements would best reflect the null hypothesis that coefficient of the first independent variable is equal to 1.0?

A. Since the calculated t-statistic exceeds the critical t-statistic of 1.68, the null hypothesis is rejected.

B. Since the calculated t-statistic of 2.88 exceeds the critical t-statistic, the null hypothesis is rejected.

C. Since the calculated t-statistic of 6.88 falls within the critical t-statistic, the null hypothesis is accepted.

Correct Answer: B

1. Set up the two-tailed t-test. H

_{0}: b_{1}= 1 versus H_{1}: b_{1}<> 1.2. Compute the calculated t-statistic: t

_{calc}= (1.72 - 1.0)/0.25 = 2.88.3. Compute the critical t-statistic (d of f = 50 - 3 - 1) t

_{0.25, 46}= 2.013.4. Decision: since the calculated t-statistic is greater than the critical t-statistic, the null is rejected. Therefore, the coefficient of the first independent variable is not equal to 1.0.

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**User Contributed Comments**
5

User |
Comment |
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grewei |
Wouldn't the critical t-statistic be between 2.000 and 2.021? The answer (B) is the same but I come up with a different critical t-statistic. |

noonah |
Should not we use the F-statistic since it is a multiple regression? |

noonah |
Oops, discard above comment. We can use the t-statistic since we are testing the significance of only one indep. variable, rather than ALL of them. |

aruffo |
What formula is being used to calculate the t-test here? |

awbronson |
@aruffo me thinks... {B(hat) - B)} / Stand Error of B(hat) .... pg 298 in print CFA curriculum |