CFA level 2: Quantitative Methods 2020

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This channel is targeted at candidates for the CFA™ (Chartered Financial Analyst) Level 2 2020 exam.

Analysis of Variance (ANOVA) Table Explained

ANOVA (Analysis of Variance) tables are a very important part of the Level II curriculum on quantitative methods. ANOVA stands for Analysis of Variance; it helps to understands how well a model does at explaining the dependent variable.

Topics Discussed
1. RSS (Regression Sum of squares)
2. SSE: sum of Squared Errors
3. TSS: Total Sum of Squares

TSS= RSS+SSE

As expected, the total variation is equal to the sum of the explained variation and the unexplained variation:

SST=RSS+SSE
Note that the CFA does not require candidates to be able to compute this values (it would take too long) but I thought that having the definitions helps understanding the concepts.

From these values, we can get the first important statistic we want to look at when discussing the quality of a regression model:

R squared ( Coefficient of determination)=RSS/SST
The R square measures the part of the total variation that is being explained by the regression model. Its value is bounded from 0 to 1, and the closer it gets to 1 the better the model fits the real data.

Now we also want to compute the average of RSS and SSE (the mean sum of squares):

MSR=RSS/k
MSE=SSE/n−k−1
where n is the size of the sample and k is the number of dependent variables used in the model.

F stat=MSR/MSE
F is a random variable distributed under an F-Statistic with k degrees of freedom in the numerator and n−k−1 degrees of freedom in the denominator.


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