- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 3. The standard error of estimate and the coefficient of determination

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**CFA Practice Question**

Which of the following statements is (are) true with respect to the standard error of estimates?

II. If the dependent variables are normally distributed, it can be concluded that 68% of all possible future observations will lie within one standard error of estimate of the regression line.

III. The standard error of estimate may be used to compute confidence intervals around historical data and projected data.

IV. The standard error associated with a predicted value for the dependent variable will always be greater than the standard error of estimate.

I. In essence, the standard error of estimate gives an indication as to how imperfect the regression model is.

II. If the dependent variables are normally distributed, it can be concluded that 68% of all possible future observations will lie within one standard error of estimate of the regression line.

III. The standard error of estimate may be used to compute confidence intervals around historical data and projected data.

IV. The standard error associated with a predicted value for the dependent variable will always be greater than the standard error of estimate.

Correct Answer: I and IV

II is incorrect because if the dependent variables are normally distributed, it can be concluded that 68% of all "historical observations" will lie within one standard error of estimate of the regression line. Consequently, (III) is incorrect as well.

IV is correct because when predicting values for the dependent variable, there are other sources of error in addition to the standard error of estimate. Namely, the regression equation itself is a composite of variables. Hence, the errors associated with the regression coefficient can cause greater dispersion between the predicted values for the dependent variable and its actual outcome.

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**User Contributed Comments**
3

User |
Comment |
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amamed213 |
please, can someone explain more why IV is correct ? |

davidt876 |
i've googled far and wide and I think this is just a case of unclear wording by analyst notes... there is a lot of inconsistent usage of the term "standard error" online - anyone able to clarify what they sayin? |

davidt876 |
i actually just tried to test IV with the data set in this guys video (https://www.youtube.com/watch?v=r-txC-dpI-E) and it didn't hold true. I assumed the "standard error associated with a predicted value" was the standard deviation of y-hat (0.95) divided by the sqrt of n (5) which gave me 0.42 - and that's lower that the standard error of estimation calculated of 0.89. anyone? |