What is R2

with notations
SSR = Sum of Squares REGRESSION
SSE = Sum of Squares ERRORS
SST = Sum of Squares TOTAL

Question

What is R2 
 
with notations 
SSR = Sum of Squares REGRESSION
SSE = Sum of Squares ERRORS
SST = Sum of Squares TOTAL

BlackTom AI · Accepted Answer

The question concerns the R-squared statistic in regression, with the following notations: SSR is the sum of squares of regression, SSE is the sum of squares of errors, and SST is the total sum of squares. By definition, SST = SSR + SSE, and R2 is commonly defined as the proportion of total variation explained by the model. This leads to R2 = SSR / SST, which is also equal to 1 − (SSE / SST).

Option 1: '1-SST/SSR' would represent 1 minus SST divided by SSR, which is not a standard or meaningful expression for R2 in this context and does not relate to the correct relationship between SSR and SST.

Option 2: '1-SSR/SSE' subtracts the ratio SSR/SSE from 1. This does not align with the decomposition SST = SSR + SSE, and it does not produce the fraction of variance explained (R2).

Option 3: '1 - SSE' subtracts SSE from 1, which mixes a unitless probability-like value with an unchanged scale; SSE is in the same squared units as the data, so subtracting it from 1 is not a valid expression for R2.

Option 4: 'SSR/SST' expresses the ratio of the regression sum of squares to the total sum of squares, which by the definitions SST = SSR + SSE indeed equals R2 (since SSE/SST is the unexplained portion and SSR/SST is the explained portion). Therefore SSR/SST is the correct formulation for R2 in this context.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 11. Quiz for Class 11

What is R2 with notations SSR = Sum of Squares REGRESSION SSE = Sum of Squares ERRORS SST = Sum of Squares TOTAL

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