Linear Regression R2
Parameters:
- Source: The data source for the calculation.
- Open Price: Uses the opening price of each period.
- High Price: Uses the highest price of each period.
- Low Price: Uses the lowest price of each period.
- Close Price: Uses the closing price of each period.
- Volume: Uses the trading volume of each period.
- Weighted: A weighted price is typically calculated as (High + Low + Close + Close) / 4.
- Typical: Calculated as (High + Low + Close) / 3.
- Median: Calculated as (High + Low) / 2.
- Periods: This parameter controls the number of periods used to calculate.
Style:
- Customizable options for visual representation (line color, style, etc.)
The Linear Regression R2, often called R-squared, is a statistical measure in technical analysis that is used to represent the percentage of a security's price movements, which fluctuations in a related variable or index can explain. This measure is derived from linear regression, a basic form of predictive analysis used to model relationships between variables.
Basics of Linear Regression Linear regression analyzes the connection between two variables by applying a linear equation to the data observed. It treats one variable as independent and the other as dependent. For instance, the independent variable in financial markets might be time, and the dependent variable might be the stock price.
How Linear Regression R2 Works: R-squared is calculated from the linear regression model. The coefficient of determination is represented as 𝑅2, which is the square of the correlation coefficient 𝑅. This value indicates the percentage of the dependent variable's variation that is explained by the independent variable. It indicates the percentage by which the independent variable explains changes in the dependent variable.
R^2 = 1 - (SSres / SStot)
- SSres (sum of squares of residuals): The sum of the squares represents the collective squared differences between predicted values and actual values, calculated vertically.
- SStot (total sum of squares): The sum of the squared differences between each actual value and the mean of these values
The R-squared value is measured on a scale that begins at 0 and extends to 1. This scale indicates:
- 0 signifies that the model does not account for any of the variability observed in the response data relative to its average.
- 1 implies that the model accounts for the entire range of variability seen in the response data relative to its average.
Key Aspects of Linear Regression R2:
- Measure of Fit: R-squared measures how well the model fits the data. Higher R-squared values represent a better fit.
- Predictive Accuracy: It assesses the strength of the linear regression model's prediction. A higher R^2 value generally indicates a more reliable model for making predictions based on the given independent variable.
- Dependency on Variable: The interpretation of R2 depends heavily on the context and the analyzed variables. It does not convey the appropriateness of the model nor whether the predictions are biased.
Application in Trading: In trading, R-squared is used to determine the strength of a trend. A higher R-squared value implies a strong trend, and that future price movements are highly predictable based on the trend line. It can be particularly useful for trend-following traders to validate their strategies.
Limitations:
- Overfitting: A high R-squared value might result, especially in models with many predictors.
- Non-linear Relationships: R-squared only measures the strength of linear relationships. It is not an effective metric for non-linear relationships that might be more appropriate for describing financial market data.
- Directionality: R-squared does not provide information on the direction of the relationship (whether positive or negative).
Conclusion: The Linear Regression R2 is a vital statistical tool in financial analysis, providing insights into the predictability and strength of financial trends based on past data. While it is a powerful tool for assessing the quality of a linear regression model, traders should use it alongside other indicators and models to account for its limitations, particularly its ineffectiveness in identifying non-linear patterns that are common in financial data.