CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance
An analyst builds a prediction interval for a dependent variable using a simple linear regression. Holding the confidence level and the estimated model fixed, the standard error of the forecast is most likely smallest when the value of the independent variable used for the forecast is:
The forecast standard error is smallest when the independent variable equals its sample mean. The forecast error includes a term that grows with the squared distance of the forecast value from the mean, so predictions near the center of the data are more precise than those far from it.
- Aequal to the sample mean of the independent variableCorrect
- Bone standard deviation above the sample mean
- Cfar outside the range of the sample observations
Explanation
The forecast standard error includes a term proportional to (X_f − mean X)², so it is minimized at the sample mean. Moving away from the mean, especially outside the sample range, widens the interval.
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