OpenIntro Statistics is an excellent resource for a clear chapter on regression analysis:
Diez, D. M., Barr, C. D., & Cetinkaya-Rundel, M. (2012). OpenIntro Statistics. Chapter 8 - Linear Regression.
The Teacups, Giraffes & Statistics site has nice explanations of variance, covariance, and the standard error.
If you need a refresher on stats, you can try one of the free online statistics courses on Khan Academy, EdEx, Coursera, Udacity or other sites, or visit the OpenStax free Introductory Statistics textbook and review:
Regression is a tricky topic to learn because the math is the same across all fields, but statisticians, econometricians, and other social sciences use very different notation to describe models. Finding textbooks that suits your background and your learning style will help you in the long run.
The lecture notes for this class will focus on the principles of basic regression - the main branch in quantitative evaluation. We intentionally try to condense the topics covered so that you can develop an understanding of how a handful of core concepts all fit together (slopes, residuals, standard errors, hypothesis testing, control variables, and bias).
As a result, lecture notes are good for understanding these topics, but will not include all of the relevant background concepts and all of the formulas, not reference more advanced models. It is good to find a textbook that you are comfortable with so you can review concepts and look something up. I have a couple on my shelf that I return to often to look up formulas or read-up on a model I am not familiar with.
If you want to invest in a textbook, these are some texts that present this content using algebra instead of calculus or matrix algebra notations.