April 10, 2013
This blog is an attempt to simplify linear regression for students appearing for FRM as well as CFA® Program level 1 exam. Linear regression was a nightmare for me while I was preparing for my FRM exams. Although the internet is filled with the content of linear regression but most of the content is too mathematical and is not written with a CFA® or FRM perspective in mind. This blog has been written to fill that void. I hope you will get a comprehensive understanding of the topic after going through the blog. We are also going to have a FREE WEBINAR on the same topic where you can get a detailed analysis of the topic including discussion of some relevant questions pertaining to the topic. Also you can go through our FREE QUIZ on this topic to gauge your understanding of Linear Regression Analysis.
Linear Regression Analysis is one of the key topics in Quantitative section of FRM level 1 Exam. It is definitely one of the topics where the return on investment is high. We can expect to have around 2 or 3 questions (probably more) which canâ€™t be solved without knowing the concepts of Linear Regression Analysis. I will take you through the key concepts of Linear Regression Analysis which would help you in cracking this part of FRM level 1 exam.
It sounds simple right. We are basically trying to understand the factors on which a variable called dependent variable depends upon. If the dependent variable can be explained by using a single independent variable then the regression is called a Regression with a single regressor. If the dependent variable depends upon more than one independent variable then the regression is called Regression with multiple regressors. Very basic stuff.
Regression with a single regressor can be represented by the following equation:
You must be wondering what the error term stands for??
Where yi is the actual value, Å¶ is the predicted value using regression and á¿© is the mean value
â€“ Measures the variation of the yi values around their mean y
â€“ Variation attributable to factors other than the relationship between x and y
â€“ Explained variation attributable to the relationship between x and y
Total Variation is made up of two parts:
The Coefficient of Determination R2 The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variable. The coefficient of determination is also called R-squared and is denoted as R2
In a simple two-variable regression, the square root of R2 is the correlation coefficient (r) between X and Y.
Standard Error of Regression
P.S. In case of any queries feel free to drop in as a comment. Go through the Quiz on this topic to gauge your understanding of the topic. You can also attend the FREE Webinar on the same topic where we will also cover linear regression with multiple regressors and also discuss the questions of the QUIZ.
Details of the FREE Webinar on Linear Regression Analysis
This session will deal with: