Linear Regression
Select a dataset to begin
How to Use
1. Choose a data set.
2. Click "Edit Samples." Try dragging and dropping data points.
3. Click "Line of Best Fit On." Try dragging and dropping data points again. See how the Line of Best Fit changes.
4. Click "Show Explanation." Click on a column in the table to learn more. Click "Visualize" for a visual explanation of the parameter.
Regression Table
| \(\displaystyle{n}\) | \(\displaystyle{\bar{\cssId{xMEAN}{x}}}\) | \(\displaystyle{\bar{\cssId{yMEAN}{y}}}\) | \(\displaystyle{\hat{\cssId{BETA0}{B_{0}}}}\) | \(\displaystyle{\hat{\cssId{BETA1}{B_{1}}}}\) | \(\displaystyle{SEE}\) |
Sample Size
Sample size is the number of data points. Sample size is defined mathematically as the following:
$$n$$X Mean
X mean is the average value of the x data. X mean is defined mathematically as the following:
$$\bar{\cssId{xMEAN}{x}}= \sum_{i=1}^{\cssId{sampleSize}{n}} \dfrac{\cssId{xi}{x_{i}}}{n}$$Y Mean
Y mean is the average value of the y data. Y mean is defined mathematically as the following:
$$\bar{\cssId{yMEAN}{y}}= \sum_{i=1}^{\cssId{sampleSize}{n}} \dfrac{\cssId{xi}{y_{i}}}{n}$$Beta 0
Beta 0 is the y intercept of the regression line. The current beta 0 estimate has a variance of __. Beta 0 is defined mathematically as the following:
$$\hat{\cssId{BETA0}{B_{0}}}= \bar{\cssId{yMEAN}{y}}- \hat{\cssId{BETA0}{B_{1}}} \bar{\cssId{xMEAN}{x}}$$Beta 1
Beta 1 is the slope of the regression line. The current beta 1 estimate has a variance of __. Beta 1 is defined mathematically as the following:
$$\hat{\cssId{BETA1}{B_{1}}}= \dfrac{\cssId{sxy}{S_{xy}}}{\cssId{sxx}{S_{xx}}}$$Sum of Squared Errors
Sum of squared Errors is the sum of the square residuals. SSE is defined mathematically as the following:
$$SEE = \sum_{i=1}^{n} \Big{(}y_{i}-\big{(}\hat{B_{0}}+ \hat{B_{1}}x_{i}\big{)}\Big{)}^{2}$$