- 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:

At a significance level of 5%, which of the following statements would best reflect the significance of the regression coefficients together as a whole?

A. The calculated F-statistic is greater than the critical F-statistic of 7.25, thus making the model significant.

B. The calculated F-statistic of 13.71 is inside the bound of the acceptance range, thus making the model insignificant.

C. The calculated F-statistic of 13.71 is outside the bound of the acceptance range, thus making the model significant.

**Explanation:**1. Set up the test (F-test):

H

_{0}: b

_{1}= b

_{2}= b

_{3}= 0.

Hb

_{1}: At least one of the coefficients does not equal to 0.

2. Compute the 'Calculated F': F

_{calc}= MSS

_{R}/MSS

_{E}= 7391/539 = 13.71.

3. Compute the 'Critical F'. F

_{calc}at the 5% significance level with a d of f(MSS

_{R}) = 3 (numerator) and d of f(MSS

_{E}) = 46 (denominator) equals: (approximately) 2.81.

4. Decision: since the calculated F statistics is greater than the critical value, the null hypothesis is rejected. Thus, at least one of the coefficients does not equal 0, giving the regression equation significance.

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