R Hoch 2 Statistik

The Coefficient of Determination

What is the Coefficient of Determination?

The coefficient of determination, also known as R-squared (R²), is a statistical measure that indicates the strength of the relationship between two variables. It is a measure of how well a regression model fits a set of data, and is calculated as the square of the correlation coefficient between the predicted values and the observed values.

Interpretation

R² ranges from 0 to 1, where:

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• 0 indicates no linear relationship between the variables.
• 1 indicates a perfect linear relationship between the variables.

A higher R² value indicates a stronger linear relationship between the variables. However, it is important to note that R² only measures the strength of the linear relationship, not the direction of the relationship.

Limitations

While R² is a useful measure of the strength of a linear relationship, it has some limitations:

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• It only measures the linear relationship between variables.
• It can be misleading if the relationship between the variables is non-linear.
• It can be affected by outliers.
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• It should not be interpreted as the percentage of variance explained by the model.

Conclusion

The coefficient of determination is a valuable statistical measure for assessing the strength of the linear relationship between two variables. However, it is important to note its limitations and interpret it correctly to draw meaningful conclusions from the data.