R squared from residual and regression sums of squares

Question

After fitting an OLS regression, the residual (error) sum of squares is $\text{SSE}=120$ and the regression (explained) sum of squares is $\text{SSR}=80$ . Find $R^2$ .

Short answer

$2/5$ . For OLS with intercept the total sum of squares splits as $\text{SST}=\text{SSR}+\text{SSE}=200$ , so $R^2=\text{SSR}/\text{SST}=80/200=0.4$ .

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Lessons behind this question

Simple Linear Regression: OLS Estimators and Geometry
Multiple Linear Regression
Populations, Samples, and Sampling Distributions

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