- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 4. Confidence intervals for regression coefficients

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**CFA Practice Question**

A regression equation that is derived from ten historical observations is given as follows:

B. The upper limit of the estimate for the regression coefficient is 1.98.

C. The lower limit of the estimate for the regression coefficient is 0.45.

If the standard error of the y-intercept is 1.26 and the standard error of the regression coefficient is 0.58, using a 10% significance level, which of the following statements would be incorrect?

A. The lower limit of the estimate for the y-intercept is -0.55, and the upper limit is 4.13.

B. The upper limit of the estimate for the regression coefficient is 1.98.

C. The lower limit of the estimate for the regression coefficient is 0.45.

Correct Answer: B

for b

for b

Use a t-test to define the acceptance range: t

_{0.1/2, 8}= 1.860. Also, the degrees of freedom = n - 2 = 8.Therefore, the ranges are as follows:

for b

_{0}= 1.79 +/- 1.86 (1.26) = -0.55 to 4.13.for b

_{1}= 1.53 +/- 1.86 (0.58) = 0.45 to 2.61.###
**User Contributed Comments**
10

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

Danny20082 |
The question did not specify the number of observations. |

MonkeySee |
First line: "A regression equation that is derived from ten historical observations..." |

investoprenuer |
How can it be B? The isn't the upper limit for b1 2.61. Ans B is 1.98 |

investoprenuer |
Sorry.... incorrect.... Got it. |

shajidubai |
how did you get 1.98? |

Adi8232 |
lol, chill guys, looks like stress is making your thinking fuzzy. |

shash0678 |
How did we get 1.98? |

bablig |
The queston says which is incorrect...1.98 is INCORRECT. |

ashish100 |
No chill how did they get 1.86? |

zagorny95 |
t table - look for 10% two tail significance level [5% if 1 tail table] for 8 degrees of freedom - Table gives you the result of 1.86 |