Example 1
\(\text{Points: } (1,2), (2,4), (3,5), (4,4), (5,5) \rightarrow y = 0.6x + 2.2, R^2 = 0.64\)
Linear Regression
Perform linear regression analysis with correlation and prediction
Results
Enter values and click Calculate to see the result.
Linear Regression
Linear regression finds the best-fitting straight line through a set of data points using the least-squares method.
- Slope (m): The slope of the regression line; how much y changes per unit change in x.
- Intercept (b): The y-value where the line crosses the y-axis (when x = 0).
- R²: Coefficient of determination; the proportion of variance in y explained by x (0 to 1).
- Correlation (r): Pearson correlation coefficient measuring strength and direction of the linear relationship (−1 to +1).
The regression line is the straight line that minimizes the sum of squared vertical distances from the data points.
\(y = mx + b, m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}, b = \bar{y} - m\bar{x}\)
Worked Examples
Example 2
\(\text{Study hours vs test scores} \rightarrow \text{Find relationship and predict outcomes}\)