CFA charterholders understand the importance of satisfying the assumptions underlying simple or multiple linear regressions to make reliable estimates and forecasts in their investment recommendations, decisions and actions.
This RapidDigest only includes what is covered in the 2021 CFA® Curriculum Readings (Readings 4 and 5).
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Formulation
single:

multiple:

Assumptions, Breach Detection and Correction
Assumptions 
If Breached 
Tested and Corrected 
1. linear relation of X and Y  transform X and/or Y or use another method  
2. nonrandom X

can still use the method if X not correlated with ε (unconditional heteroskedasticity)


or X's (no perfect collinearity) 
multicollinearity 

3. error term  
a. normal distribution  
b. mean = 0 


c. variance = constant 
ε correlated with X:


d. correlation = 0 
serial correlation


Application to RealWorld Data
Data Source: OECD
Regression Assumptions In Action
Can you see where the regression assumptions are in action?
Assumptions 
In Action 
1. linear relation of X and Y  upward sloping line 
2. nonrandom X  Vertical base of the bell curve corresponds to a particular X value. 
3. error term  Each observation has a bell curve. 
a. normal distribution  Distance of actual value from predicted value of each observation represents the distribution of errors, which is normal; hence, the bell curve. 
b. mean = 0  The center of each bell curve is the mean of prediction error so that each observation is predicted to fall on the regression line. 
c. variance = constant 
Each bell curve, being normal distribution shape, has variability defined by standard deviation, which if squared is the variance. Bell curves, being same size and shape, are identical across actual observations. 
d. correlation = 0  not shown 
Understand the Why
For valid estimation and forecast, the regression assumptions must be held and observed; else the regression model is unreliable because statistical tests are invalid.
RealWorld Practical Application
https://www.fool.com/investing/2019/05/22/doesesginvestingproducebetterstockreturns.aspx
RapidInsight: Scatter Plot Before Regression
 Residuals appear to grow larger as ROIC increases (i.e. conditional heteroskedastic?)
 Understated regression standard errors inflate the tstatistic that increases Type I error (i.e. ROIC is significant predictor of EV/IC when it is actually not).
 Further Reading Digest: Linear Regression (Analysis)
RapidInsight: Established Equations Have High Linear Relationship
ROIC reflects Earnings Per Share (EPS); whereas EV/IC, as described, is PricetoBook ratio. The denominator of both ratios pertains to equity so that they cancel out leaving the relationship of Earnings and Price: either E/P as earnings yield or P/E ratio. Since earnings drive stock prices and intrinsic values then their R^{2} is necessarily high. 