1. Coefficient of Determination- R²
Statistical Inference for Managers By
Imran Khan

2. The total variability in a regression SST, can be partitioned into a component explained by the regression SSR and a component due to unexplained error SSE.
SST=SSR+SSE
Total sum of squares SST=
Error sum of squares SSE=
Regression sum of squares SSR=
Graph

3. Coefficient of Determination
R² measures the proportion of variation in the dependent variable Y explained by the regression model.
R²= SSR/ SST= 1-SSE/SST
SSR=
R² increases directly with the spread of independent variable.
0<R²<1
Greater the R², better fitted is the model

4. σ²= S²e=Σei²/n-2=SSE/n-2
Correlation and R²
R² for simple regression is equal to correlation squared.
R²= r²
Estimation of model Error Variance
σ²= S²e=Σei²/n-2=SSE/n-2

5. Example
Find and interpret the coefficient of determination for the regression of stereo system sales on price, using the following data: Sales Price