- CFA Exams
- CFA Exam: Level II 2021
- 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**

You have obtained the following sample regression equation from 25 samples:y-hat

_{t}= 2.304 + 3.412X

_{t1}- 4.657X

_{2t}

The estimated standard errors are 0.87, 1.23 and 1.78 for b

_{0}, b_{1}and b_{2}, respectively. Let α = 0.05. Would you reject H_{0}: β_{1}<= 0 against H_{1}: β_{1}> 0?

Correct Answer:

t-statistic = (3.412 - 0)/1.23 = 2.77.

The critical value of t having 22 degrees of freedom is 1.717.

As 2.77 > 1.717, we would reject the null hypothesis.

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

t-statistic = (3.412 - 0)/1.23 = 2.77.

The critical value of t having 22 degrees of freedom is 1.717.

As 2.77 > 1.717, we would reject the null hypothesis.

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**User Contributed Comments**
7

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

soniamoren |
But the t value is calculated with the standard error not the standard deviation |

katybo |
that is right! |

danlan2 |
use p=0.05 since it's one tail test. |

DBBrian |
If H0:B1=0, why it is not a two tail test? In addition, does it make sense that the null hypothese (B1=0) and the alternative hypothese (B1 > 0) not covering all scenario. How about (B1 < 0) ? |

Vonoko |
2.77 is way out - no need to think about the two-tailed or not. Besides n is 25. Generally, if n>30 t-statistic critical values are close to z-critical values (standard normal). For z as you remember 1.96 is the 2.5% |

cfaajay |
It is a Two tailed test and t he confidence interval at 5% level of significance will be +/- 2.074 ,and hence you will reject the null Hypothesis .whenever the null hypothesis include equality then test will be two tailed . Vonoko ,you are right in saying that @ 5% two tailed z value will be 1.96 ,but as it is t test the confidence interval should bw wider and hence its +/- 2.074. Stick to what you know. |

Oksanata |
it's a one tail test, but the t-critical should be 2.074 (according to the logic of previous quest.1) |