Chartered Financial Analyst (CFA) Practice Exam Level 2

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What is the relationship between the total sum of squares (SST), sum of the squares due to regression (SSR), and error sum of squares (SSE)?

SST = SSR - SSE
SST = SSR + SSE
SST = SSR * SSE
SST = SSR / SSE

The correct answer is: SST = SSR + SSE

The total sum of squares (SST), sum of the squares due to regression (SSR), and error sum of squares (SSE) are fundamental concepts in regression analysis that describe how the variability in a dataset can be partitioned. The relationship that SST = SSR + SSE is derived from the principle of partitioning the total variance in the dependent variable. SST represents the total variability in the dependent variable, which can be attributed to two sources: the variability explained by the regression model (SSR) and the unexplained variability, or error (SSE). By this framework, SSR quantifies how well the independent variables in the model explain variance in the dependent variable, while SSE captures the error or residual variance that remains after accounting for the effect of the independent variables. Since the total variability is made up of the explained and unexplained components, the correct relationship is that the total sum of squares is equal to the sum of the squares due to regression and the error sum of squares. In essence, this relationship helps in assessing the goodness of fit of the regression model; if SSR is significantly large compared to SSE, it indicates that the model explains a large portion of the variance in the dependent variable.