P1.T2. Pg 9 Stock and Watson Reading 11 Study Notes

[Dr. Jayanthi Sankaran]

Hi David,

In page 9 of the above it is mentioned that "Correlation (dependence) is not causation. Further, linear correlation is a specific type of dependence, which is a more general relationship (e.g. non-linear relationship).

I don't quite understand the colored statement. This section pertains to 'Linear regression with one Regressor'. When you talk about non-linear relationship, are you talking about some kind of variance-covariance matrix with a non-linear correlation structure? Sorry, this is kind of confusing.

Thanks!
Jayanthi

 

[Dr. Jayanthi Sankaran]

Hi David,

Just occurred to me that you are, possibly, saying that while the correlation parameter is linear, the variables may have a non-linear relationship. Please clarify!

Thanks!
Jayanthi

 

[ShaktiRathore]

Yes jayanti
As dependence encompasses both linear and non linear correlations,therefore linear correlation is a specific type of dependence.Dependence is a set of {linear correlation,non linear correlation} so linear correlation being a subset of dependence set means linear correlation is a specific type of dependence. Dependence is more general it can imply linear or non linear correlation where linear correlation is a special type of dependence. A linear correlation of 0 does not imply independence bevause some non linear correlation is still possible therefore dependence is not ruled out but independence do imply linear correlation of 0.
Thanks