- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 5. Multiple Regression
- Subject 4. The Standard Error of Estimate in Multiple Linear Regression Model

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**CFA Practice Question**

Which of the following statements is (are) true with respect to the standard error of estimate of a multiple linear regression model?

II. Each residual produced by the model is equal to the difference between the actual value of the dependent variable and its mean.

III. As the number of independent variables included in the model increases, the standard error of the residuals will decrease.

IV. The mean of the residuals produced by a multi linear regression model will always equal to zero.

I. The standard error of the residuals resulting from the regression model is in essence, the standard error of estimate of the regression model.

II. Each residual produced by the model is equal to the difference between the actual value of the dependent variable and its mean.

III. As the number of independent variables included in the model increases, the standard error of the residuals will decrease.

IV. The mean of the residuals produced by a multi linear regression model will always equal to zero.

A. I and IV

B. II and IV

C. II and III

**Explanation:**II is incorrect because each residual produced by the model is equal to the difference between the actual value of the dependent variable and the estimated value for that dependent variable produced by the model.

III is incorrect because the standard error of the residuals is as follows:

SEE = [SSE/(n - k - 1)]

^{1/2}, therefore, as k increases, the whole term will increase.

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**User Contributed Comments**
2

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

ThePessimist |
Also, III is generally wrong, since while K will increase, SSE will usually go down with additional independent variables. |

dblueroom |
ThePessimist - SSE probably will go down, but at insignificant rate. This is a good question. |