Enter the sum of the square of residuals and the total sum of squares into the calculator to determine the coefficient of determination.
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Coefficient of Determination Formula
The following formula is used to calculate the R squared or the coefficient of determination.
R^2 = 1 - (RSS/TSS)
- Where R2 is the coefficient of determination
- RSS is the sum of squares of residuals
- TSS is the total sum of squares
To calculate the coefficient of determination, divide the sum of squares of residuals by the total sum of squares, then subtract the result from 1.
FAQ
What does the sum of squares of residuals (RSS) represent?
The sum of squares of residuals (RSS) represents the variation in the dataset that is not explained by the model. It’s a measure of the discrepancy between the data points and the model’s predicted values.
How is the total sum of squares (TSS) calculated?
The total sum of squares (TSS) is calculated by taking the sum of the squared differences between each data point and the mean of the dataset. It represents the total variation in the dataset.
Why is the coefficient of determination important in statistical analysis?
The coefficient of determination is important because it provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. It helps in determining the strength of the relationship between the model and the observed data.