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Coefficient of Determination - R Squared - Time-Series Prediction

by The trader, 1998 days ago
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In statistics, the coefficient of determination represents the strength of the relationship or the portion of common variation in two time-series or variables. It is a statistical measure of how well the regression line approximates the real values.


The coefficient of determination or RČ is mainly used to analyze how well a variable can predict another one. The returned value gives us the percentage of change of variable X that can be explained by changes in variable Y.
The coefficient of determination is calculated by taking the square of the Pearson correlation (simple linear correlation). A value of 1 or 100% indicates that moves in one time-series can be entirely explained by the second time-series, while a value of 0 or 0% means that that the first time-series cannot be explained by moves in the second time-series. RČ values range from 0 to 1.

Example:
The correlation between the weekly change of the S&P 500 Index (Ticker Symbol: ^GSPC) and the previous week change for the last 50 trading weeks is equal to 0.13.
The coefficient of determination is equal to 0.0169 or 1.69%, which means that weekly changes can explain only 1.69% of next week changes.

Formula Example:
a = r2(perf(close, 1), perf(close[1], 1), 50);
plot(a, "", colorGreen);

Calculate RČ of the current and previous rate of change using the last 50 trading bars.
Plot the coefficient of determination of each trading bar on a chart.


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