# On Least Squares Linear Regression Without Second Moment

### Abstract

If *X* and *Y* are real valued random variables such that the first moments of *X*, *Y*, and *XY* exist and the conditional expectation of *Y* given *X* is an affine function of *X*, then the intercept and slope of the conditional expectation equal the intercept and slope of the least squares linear regression function, even though *Y* may not have a finite second moment. As a consequence, the affine in *X* form of the conditional expectation and zero covariance imply mean independence.

**Minnesota Journal of Undergraduate Mathematics**, [S.l.], v. 4, n. 1, june 2018. ISSN 2378-5810. Available at: <https://mjum.math.umn.edu/index.php/mjum/article/view/72>. Date accessed: 14 july 2020.