Reading 11, 3.3 Standard Error of Estimate

Level 2, Volume 1, Quantitative Methods, Reading 11, Correlation & Regression

The references refer to the CFA text book.

3.3 The Standard Error of Estimate

Recall that the Standard Error of Estimate (SEE) it is a part of the linear regression formula, as shown below:

The standard error of estimates is a measure of the accuracy of predictions made by linear regression methods. It represents the portion of the dependent variable that cannot be explained by the independent variable.

The formula for the standard error of estimate (SEE) for a linear regression model with one independent variable is =

 

Some comments

This statistic is very much like the standard deviation for a single variable, except that it measures the standard deviation of   ê_i, the residual term in the regression.

The SEE formula looks very much like the formula for computing a standard deviation, except that n - 2 appears in the denominator instead of n - 1. We use n - 2 because the sample includes n observations and the linear regression model estimates two parameters (bˆ0 and bˆ1); this difference is also called the degrees of freedom; it is the denominator needed to ensure that the estimated standard error of estimate is unbiased. (Check Reading 11, 3.2 for the assumptions of Linear regression)

Example
(Link to Excel file on box.net)

1. Data
Year	2010	2009		2008		2007		2006
Revenue US $m	52798	50211		59473		47473		39099
Earnings per ordinary share - declared in respect of the period (US cent)	227.8	105.4		274		228.9		172.4

Year	Revenue $ (X)	Earnings - Expected based on regression analysis in 3.1	Earnings - Actual		Cross product
2010	52798	215.22	227.8		158.18
2009	50211	203.65	105.4		9653.11
2008	59473	245.08	274.8		883.11
2007	47473	191.40	228.9		1406.09
2006	39099	153.94	172.4		340.70
Sum					12441.20
(N-2)					3.00
Answer					4147.07
Standard error					64.40