Example 1
\(\text{Points: } (1,2), (2,4), (3,5), (4,4), (5,5) \rightarrow y = 0.6x + 2.2, R^2 = 0.64\)
線形回帰計算機
散布図の視覚化でデータの最適な直線を見つける
結果
値を入力して計算をクリックして結果を表示してください。
Linear Regression
Linear regression finds the best-fitting straight line through a set of data points. The line is defined by the equation y = mx + b, where:
- Slope (m): The rate of change in y for each unit change in x
- Intercept (b): The value of y when x = 0
- R² (R-squared): Coefficient of determination (0 to 1), indicates how well the line fits the data
- Correlation (r): Measures the strength and direction of the linear relationship (-1 to 1)
The regression line minimizes the sum of squared differences between observed and predicted values (least squares method). An R² value close to 1 indicates a strong linear relationship, while a value close to 0 suggests a weak relationship.
\(y = mx + b, m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}, b = \bar{y} - m\bar{x}\)
Worked Examples
Example 2
\(\text{Study hours vs test scores} \rightarrow \text{Find relationship and predict outcomes}\)