- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 9. Using Dummy Variables in Regressions

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**CFA Practice Question**

Suppose data from a large corporation are used to estimate a regression model that explains the corporation's salary structure. The estimated equation is y-hat

Question 2: Suppose a male with no college degree has been employed 5 years. Predict his salary.

Question 3: Suppose a new male recruit who has a B.A. is hired. Predict his salary.

Question 4: How would these coefficients change if we let x

_{t}= 35,000 + 3,000 x_{t1}+ 6000 x_{t2}+ 15,000 x_{t3}- 2000 x_{t4}where

- y-hat
_{t}= salary of individual t. - x
_{t1}= years of service of individual t. - x
_{t2}= 1 if highest degree is B.A for individual t, or 0 otherwise. - x
_{t3}= 1 if individual has master's or Ph.D., or 0 otherwise. - x
_{t4}= 1 if individual is a female, or 0 if individual is male.

Question 1: Suppose a female Ph.D. has been employed for 4 years. Predict her salary.

Question 2: Suppose a male with no college degree has been employed 5 years. Predict his salary.

Question 3: Suppose a new male recruit who has a B.A. is hired. Predict his salary.

Question 4: How would these coefficients change if we let x

_{t4}be 1 for a male and 0 otherwise.Correct Answer: Q1: 35,000 + 3,000 x 4 + 6,000 x 0 + 15,000 x 1 - 2,000 = 60,000.

Q2: 35,000 + 3,000 x 5 + 6,000 x 0 + 15,000 x 0 - 2,000 x 0 = 50,000.

Q3: 35,000 + 3,000 x 0 + 6,000 x 1 + 3,000 x 0 - 2,000 x 0 = 41,000.

Q4: The coefficient x

Q2: 35,000 + 3,000 x 5 + 6,000 x 0 + 15,000 x 0 - 2,000 x 0 = 50,000.

Q3: 35,000 + 3,000 x 0 + 6,000 x 1 + 3,000 x 0 - 2,000 x 0 = 41,000.

Q4: The coefficient x

_{t4}would change from -2,000 to +2,000. The intercept would decrease to 33,000.###
**User Contributed Comments**
8

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

johans |
Why would the intercept decrease to 33,000? |

webII |
for Q4 - why would the answer not be holding all other factors equal, the change would now pay a female $2000 more than a male with similar qualifications. |

nick1981 |
Incorrect webli, it would not alter any of the previous assumptions only changing perspective. |

xyzanand |
Meaning that both men and women lose 2000. So if they hire horses, they wont lose the 2000 and if the horse had phd and many years of service he would make even more. |

rhardin |
I still don't understand why the intercept decreased. I also don't understand why the PHD doesn't get credit for having a BA. I thought that was understood... if you have a PHD you have a basic college degree too. |

Quinner |
The point is that they want to know how to change the equation (coefficients) without changing the results. So you have to change the intercept. |

andynyc |
because it would then be +2000 instead of -2000 so to make Yhat the same, intercept falls. |

Mckett |
hardin I thought the same but it states if BA is the highest its 1, if they have a PHD then BA is not highest |