Scatter Plot for Regression Analysis — OLS Trendline, Slope & R² Solver
A regression scatter plot pairs bivariate observations $(x_i, y_i)$ with the analytical least-squares line $\hat{y} = mx + b$ that minimizes the sum of squared vertical residuals ($\min \sum (y_i - \hat{y}_i)^2$).
Tip: Paste Excel or Google Sheets rows (Ctrl+V / ⌘V) directly into any cell.
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Covariance: S_xy = sum((x_i - x_bar)*(y_i - y_bar)). Variance: S_xx = sum((x_i - x_bar)^2). Slope: m = S_xy / S_xx. Pearson r = S_xy / sqrt(S_xx * S_yy). R^2 = r^2.
Chart Design & Use-Case Tips
- 01Covariance: S_xy = sum((x_i - x_bar)*(y_i - y_bar)). Variance: S_xx = sum((x_i - x_bar)^2). Slope: m = S_xy / S_xx. Pearson r = S_xy / sqrt(S_xx * S_yy). R^2 = r^2.
- 02Read the exact OLS slope (m), y-intercept (b), and R² goodness-of-fit badge rendered directly in the chart studio header.
- 03Inspect whether points scatter randomly above and below the trendline (homoscedasticity) or curve systematically (indicating a polynomial or log relationship).
- 04Paste experimental lab readings directly from CSV or Excel to generate publication-ready regression plots.
Frequently Asked Questions
How is the linear regression line calculated?+
The engine computes exact closed-form Ordinary Least Squares (OLS) estimators for slope m and intercept b across all active rows, plus the exact R² coefficient of determination.
What is the relationship between Pearson's r and R²?+
In simple linear regression, R² is the square of the Pearson correlation coefficient r (R² = r²), representing the fraction of variance in Y linearly explained by X.
Can I use decimal and negative coordinates?+
Yes, both X (Series A) and Y (Series B) accept floating-point decimals and negative values.