Least Squares Line

The residual of each data point is drawn on the scatter plot, with a magnified residual plot below it. Show numbers works out the residual vector:

$$\overline{r} = \overline{y} - (m\overline{x} + b\overline{1}).$$

The panel also tracks the length $\lVert \overline{r} \rVert$ and the root mean square error (RMSE). The RMSE is $\lVert \overline{r} \rVert / \sqrt{n}$ for $n$ data points. Least squares moves the drawn line to the least squares line. Show least squares line draws the least squares line dashed for comparison and lists its $\lVert \overline{r} \rVert$ and RMSE.

Under More:

• Line comparison. Save this line adds the current line to a table of $\lVert \overline{r} \rVert$ and RMSE. A row loads its line again.
• Squared residuals. Show squares draws the square of each residual. The total area of the squares is $\lVert \overline{r} \rVert^2$.

The datasets are Twitter users, three points, US e-commerce sales and world population growth.