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**Coefficient of Determination- R²**

Statistical Inference for Managers By Imran Khan

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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

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**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

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**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

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

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Learning Objectives Copyright © 2002 South-Western/Thomson Learning Data Analysis: Bivariate Correlation and Regression CHAPTER sixteen.

Learning Objectives Copyright © 2002 South-Western/Thomson Learning Data Analysis: Bivariate Correlation and Regression CHAPTER sixteen.

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