Today being Sunday , I was walking to a local hotel to have my breakfast. I had this immense urge to pick a book and read during the time waiter serves me the breakfast and tea. However this time I resisted.

Why ? I want to ust think , ruminate over what has been going on in my mind for the last 20 odd days. It was about regression.
What my mind brought me was really a fresh thought about regression and for which I am really happy that I took the odd walk with myself

Well, If I were to explain regression in simple words here is how it will be.
If I have a Y as dependent variable and X1 X2… Xn as n independent variables, the way to look at this from a linear algebra perspective is to find the projection of Y on to column space spanned by X1…..Xn. This projection makes the error deviances minimal as the error vector would be perpendicular to the column space of X1…Xn.

So, the parameter estimates for X1…Xn have a joint normal distribution with a specific mean and standard error.
Beta = Inv(X_t*X) X_t * y

Since there is y on the RHS, there is bound to be a variation in Beta and hence beta also has a distribution.

Since beta has a joint normal distribution, one can look at covariance matrix to understand the multi collinearity