Reading 12. j Multicollinearity

The LOS reads:
"Describe multicollinearity, and discuss its causes and effects in regression analysis"


There are 4 areas that appear to be important:
1. What is multicollinearity?
2. What are the effects of multicollinearity?
3. Detecting it
4. How do you correct for it?


1. What is multicollinearity?
In Reading 11 we noted the underlying assumptions of the Linear regression model. Assumptions 2 reads as follows:

For multiple regressions we updated these assumptions, noting that the independent variables are not random and No exact linear relation exists between two or more of the independent variables. Multicollinearity is the exact opposite, being where 2 or more independent variables are highly correlated with 

each other.


2. What are the effects of multicollinearity?
Remember that heteroskadiscity & serial correlation results in standard errors that are too small?
Multicollinearity results in standard errors that are too big.
The result would therefore be the opposite.
Where the first 2 result in t-statistics that are too big, Multicollinearity results in t-statistics that are too small!


3. Detecting it
There is no statistical approach that is required to be studied for the CFA exam.
However, the following is a strong indication:
- Significant F stat, but insignificant t-stat. 
- There is a high correlation between the independent variables. (Usually when one applies your mind to the independent variables it is clear that there is high correlation)


4. Correcting it
The most obvious way is to exclude one of the independent variables from the regression.

Reading 12.i Serial correlation

The LOS reads:

"Discuss the types of heteroskedasticity and the effects of heteroskedasticity and serial correlation on statistical inference"

In the previous blog heteroskedasticity was discussed. 

Similar to the previous blog there are 4 important areas that one should master:

1. What is serial correlation

2. What are the effects of serial correlation

3. Detecting serial correlation

4. How do you correct for serial correlation

1. What is serial correlation?

In Reading 11 and earlier in Reading 12 the underlying assumptions of the Linear Regression Model were discussed. Assumption 5 relates to Serial Correlation:

The summary of the definition was:

Reading 12.i Heteroskedasticity

CFA should give bonus points to those that can spell the word Heteroskedasticity!


The LOS reads:
"Discuss the types of heteroskedasticity and the effects of heteroskedasticity and serial correlation on statistical inference"


There are 4 areas that appear to be important:
1. What is heteroskedasticity
2. What are the effects of heteroskedasticity
3. Detecting heteroskedasticity
4. How do you correct for heteroskedasticity


1. What is heteroskedasticity?
In Reading 11 & earlier in Reading 12 the underlying assumptions of the Linear Regression Model were discussed. Assumption 4 relates to Homoscedasticity, being the opposite of Heteroskedasticity.


The summary of the definition was:

(NB - Remember that Error term also refers to the Residual)

CFA Level 2, Reading 12.h, Dummy variables

I guess what makes CFA difficult is the fact that one also have other responsibilities!
2 weeks with little progress. Not good. Any way..


The LOS reads:
h. formulate a multiple regression equation by using dummy variables to represent qualitative factors, and interpret the coefficients and regression results

What is a dummy variable?

A dummy variable is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. 
For example, in econometric time series analysis, dummy variables may be used to indicate the occurrence of wars, or major strikes. It could thus be thought of as a truth value represented as a numerical value 0 or 1. (1)

(This reminds me a lot of using 0 or 1 to do computer programming at the machine level.) 

CFA Level 2, You might already know.... you are going to pass, From the New York Times

From the New York Times, an interesting article on the daily use of Significance in Statistics, and the limitations thereof.

Worth the read!