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I found a lecture notes from regression analysis but it was quite hard to learn from it. Those notes were aimed for students who had read just basics of statistics beforehand. I have a background in mathematics, read basic course of probability and measure theory/real analysis but wrote my master's thesis from algebra so I can prove theorems on my own and fill the details of reasoning.

But I would like to learn on my own what kind of methods I can use in particular situations and to improve my skills to have a job. I also like if there is some explanation why those methods works in particular situations. Those lecture notes had the following subjects:

One and two way anova, one and several explanations linear regression model, logistic regression and applying regression model to analysing the trend and seasonality.

What would one suggest to learn the topic on my own?

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    $\begingroup$ The way this question is asked suggests you are interested in the mathematical underpinnings of "regression analysis" (which is a broad, vague topic by the way) rather than in regression itself. Could you clarify this point? When you do, could you also indicate a little more precisely what you mean by "regression analysis"? $\endgroup$ – whuber Aug 19 '15 at 12:55
  • $\begingroup$ Could you tell a little bit more detailed about your background in maths? Did you study probability? You could have a look at math.stackexchange.com/questions/735075/… $\endgroup$ – kjetil b halvorsen Aug 19 '15 at 13:14
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For the basics I tend to turn to the online "Hanbook of biological statistics" The chapter on linear regression is quite simple to grasp. If you are looking for more in depth information I enjoy "Biostatistical analysis" by Zar.

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Linear regression is used in many fields. The idea is to fit a trend line to a dataset so you may predict a response variable given certain independent variables.

Say if you had some data of how many hours students study per night and their corresponding GPAs. You could use regression to predict your GPA based on how many hours you study per night. This is a simplified example and there are obviously more variables that affect GPA; so to get the most accurate prediction you would include all the variables that affect GPA.

As a math major, I would start by reading up on Ordinary Least Squares Method.

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I suggest entering your list of topics in YouTube. I have found the videos there to be very useful in learning the techniques, although more so for the general public as opposed to a Math major. One example: https://www.youtube.com/watch?v=aq8VU5KLmkY

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