v3.47: Linear Regressions Line & R² for Market Scatter Charts

Koyfin -

We’ve added a Linear Regression Line and R² value to Market Scatter charts. This line shows the overall trend between two variables, making it possible to identify relatio​​nships and predict future values.

What’s New:

  • The regression line is ON by default and can be toggled on or off using a button in the chart’s bottom-right corner.
  • Above the chart, you’ll see its equation (e.g., y = 0.1289x + 889.6705 and R² = 0.4483), which provides the trend and strength of the correlation for more precise analysis.

How It Works:

Linear Regression

  • What it is: A statistical method that models the relationship between two variables by fitting a straight line (regression line) through the data points in a scatter chart.
  • Why it’s useful: It helps to identify trends and predict outcomes. The line shows how the dependent variable (Y-axis) changes with the independent variable (X-axis).
  • Output meaning: The equation of the line (e.g., Y = mX + b) represents the relationship. Slope (m) shows the rate of change, and the intercept (b) is where the line crosses the Y-axis.

R² (Coefficient of Determination)

  • What it is: A metric that quantifies how well the regression line fits the data.
  • Why it’s useful: It identifies the proportion of variance in the dependent variable explained by the independent variable. A high R² (close to 1) indicates a strong relationship; low R² suggests weak correlation.
  • Output meaning:
    • R² = 1: Perfect fit; the model explains all variability.
    • R² = 0: No relationship; the line explains none of the variability.

Example:

The equation in the above chart, y = 0.0701x + 1.3748, represents the linear regression line.

  • y = This is the "Total Return % (10Y)" (on the Y-axis). It’s what we’re trying to estimate or predict.
  • x = This is the "Basic EPS - CO, CAGR (10Y FY)" (on the X-axis). It’s the variable we’re using to explain or predict the Y value.
  • 0.0701 (Slope): For every 1% increase in the EPS CAGR (X-axis), the Total Return (Y-axis) increases by 0.0701%.
  • If EPS CAGR goes from 10% to 11%, Total Return would rise by about 0.0701%.
  • 1.3748 (Intercept): This is the starting point of the line when the EPS CAGR is 0%.
  • If a company’s EPS CAGR is 0%, the model predicts a Total Return of 1.3748% over 10 years.

What does it mean?

The equation summarizes the relationship between EPS growth (X-axis) and Total Return (Y-axis). However, since the R² value is 0.1135 (very low), the line only weakly explains the variation in Total Return. This suggests that other factors beyond EPS growth significantly influence Total Returns for these stocks.

Watch our demo showcasing Linear Regression and R² functionality: