# Regression Analysis

#### [email protected]

##### New Member
Hi David,

Two questions regarding hypothesis testing:

(1) Autocorrelation is the correlation between 2 error terms and serial correlation is the correlation between two residual terms. Doesn't that mean that autocorrelation and serial correlation are effectively interchangeable?

(2) Would it be safe to say -- that OLS (linear regression) is where variances of the ERROR terms are constant (i.e. homoskedasticity), and multiple regression is where the error terms are STOCHASTIC, i.e. random disperson (i.e. heteroskedasticity?).

In both cases -- the independent term (x) CANNOT be correlated with the error terms (RESIDUALs for sample) whereas the dependent (Y) is allowed to be correlated with the error terms? Is that correct?

Thanks!
Eva

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Eva,

(1) Yes, interchangeable indeed! Gujarati has them as perfect synonyms (I sometimes connote serial correlation with time series as special case of regression versus autocorrelation for a generic regression, but I may have no basis)

(2) No, both univariate/multivariate OLS regression assume constant variance (homoskedastic). For both, heteroskedasticity is an assumptional violation.

Final is incorrect:
* Error term is uncorrelated with independent (X), AND
* Error term is uncorrelated with Predicted (dependent) Y
(predicted Y is a linear function of X, the second must follow from the first. Although the first only is technically the CLRM assumption)

David