# Reading 11: Correlation & Regression

One of the assumptions of the Linear Regression Model is that “the independent variable (X) is not random”. Also, the expected value of the error term = 0 Can someone please explain to me what is ment by “not random” and that the expected value of the error term is Zero? Thanks.

If it was trully random, we couldn’t explain/predict it. The whole point of linear regression is to explain/predict the independent variable using dependent variables.

Usif Wrote: ------------------------------------------------------- > One of the assumptions of the Linear Regression > Model is that “the independent variable (X) is not > random”. Yikes! Where does it say that? It’s completely false and none of the calculations for linear regression relies on any assumptions about the distribution of the independent variables. They don’t even have to have a finite mean, for example. Anyway, once the independent variables are observed why would anybody care about their distribution? (note that the distribution of the X’s may have some impact on various goodness of fit measures and especially robustness of fit measures). >Also, the expected value of the error > term = 0 > This is required. It simply means that when you have a model all the residual noise is distributed “evenly” about 0. This is a much lighter assumption than mean zero normality which is where you go as soon as you start doing t-tests and F-tests. > Can someone please explain to me what is ment by > “not random” and that the expected value of the > error term is Zero? > > Thanks.

USIF, Yes, “The Independent variable, X, is not random.” This is one of the assumptions in the linear regression model. However, the authors further explain, - Although we assume that “The Independent variable, X, is not randon”, that assumption is often clearly not true. for eg it is unrealistic to assume that monthly returns of S&P are not random. Econometricians have show that even if the independent varioable is random, we can still rely on the regression model, given the crucial assumption that the error term is uncorrelated with the independent variable. etc.etc…" So, theoritically, the assumption “The Independent variable, X, is not random.” is very much mentioned as one of the assumptions.

>So, theoritically, the assumption “The Independent variable, X, is not random.” is very >much mentioned as one of the assumptions. Although as JDV points out, it’s nonsense. Assuming that X is not random doesn’t destroy any results, however it is completely unnecessary.

So, what exactly is the reasoning behind this assumption? It is still included, could somebody maybe explain what it actually means when the independent variables are / are not random in this situation? Thanks!

Without this assumption, the model still works. But it is better that “the independent variable (X) is not random”. This assumption is badly said, but it is not wrong.

I think because it’s quite difficult to explain it in layman terms.

Honestly, I have one advice: learn it by heart. About me, I learn already by heart many things for the exam.

PS: if “the independent variable (X) is not random”, the model still works, and the beta of X will be equal to 0.

I didn’t know this expression existed in english also (apprendre par coeur) Regarding the assumption of non randomness in the independant variable, I agree with what the others have said, it’s not a necessary assumption for the linear model, but it’s often made because it simplfy the derivation of the estimators.CFAI may see it as a necessary assumption so I can’t guarantee anything for the exam

In fact, I means “learn by rote” Most of formulas in Active Portfolio Management, I must learn by rote 