- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 6. The predicted value of the dependent variable

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**CFA Practice Question**

Which of the following statements is (are) true with respect to predicting the value of a dependent variable using a regression?

II. Confidence interval around predicted values for the dependant variable will increase as the degrees of freedom increase.

III. The variance of predicted values is simply the square of the standard error of the estimate (SEE).

IV. The farther the independent variable is from its mean, the greater the dispersion will be around the predicted value for the dependent variable.

I. As the value of the independent variable increases, so will the value of the dependent variable.

II. Confidence interval around predicted values for the dependant variable will increase as the degrees of freedom increase.

III. The variance of predicted values is simply the square of the standard error of the estimate (SEE).

IV. The farther the independent variable is from its mean, the greater the dispersion will be around the predicted value for the dependent variable.

A. II and IV

B. I, II and III

C. IV

**Explanation:**A simple linear regression equation may be defined as follows:

Therefore, if the regression coefficient were to be a negative value, then as the independent value increases, the dependent value would decrease further. The confidence interval around a predicted value for Y may be defined as follows:

Therefore, as the degrees of freedom increase, the t-value will shrink; thus tightening the possible dispersion around the predicted value for Y.

The variance of predicted values may be computed as follows:

Therefore, the farther X

_{i}is from its mean, the greater (X

_{i}- X-bar)

^{2}will be, and thus the greater S

^{2}

_{f}will be. Consequently, the dispersion around the predicted value of Y will become greater.

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**User Contributed Comments**
4

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

Andrewua |
what about second? |

shival |
it is already being answered in the explanation |

chris76 |
I actually disagree with 4. The way the question is worded it seems to imply that a large x value will cause a large error in estimation. But barring conditional heteroskedacity this is simply not the case. I understand the explanation saying if there is more variance in the independent variable but this is a property of a set of numbers and not of an individual number(think if the x values were 1,2,3,4 we would not expect y^(4) to have larger error...). |

REITboy |
Andrewua - more dof --> smaller t-stat --> smaller confidence interval |