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Demystifying Linear Regression Analysis for FRM Level 1 Exam

April 10, 2013
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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 can’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.

So what is Regression Analysis??

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??

  • It represents the influence of all the variables which we have not accounted for in the equation. It may not be necessary that we will be able to figure out all the variables which affect the dependent variable. To account for that we introduce an error term.
  • It represents the difference between the actual “y” values as compared to the predicted y values from the Sample Regression Line


Method of Ordinary Least Squares (OLS)

  • b0  and  b1  are obtained by finding the values of  b0  and  b1  that minimize the sum of the squared residualsbugzilla.20
  • On finding out the second differential and equating it to zero (process not important but the result is) we get the following results.





Where yi is the actual value, Ŷ is the predicted value using regression and Ῡ is the mean value

  • TSS = Total sum of squares

–      Measures the variation of the yi values around their mean y

  • RSS = Residual sum of squares

–      Variation attributable to factors other than the relationship between x and y

  • ESS = Explained sum of squares

–      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

  • is the standard deviation of the error terms (ei) in the regression
  • Smaller the standard error, better the fit

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:

  • OLS (Ordinary least square) Regression
  • Measures of fit, Coefficient of Determination
  • Linear Regression with a single Regressor
  • Linear Regression with multiple Regressor


REGISTER FOR FREE:  click here


About the Author


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