To begin, enter your data as two columns below. Then click on the Start button below.
Use the slider to change the values for m and b. The goal for least-squares to to find values that make E2 as small as possible.
| m: | ||
| b: |
The following button uses the formula for the least-squares line.
First of all, I have made a short video that goes through a simple example using this tool. You can find the video here.
This tools is used to help understand and visualize the method of least-squares regression.
To begin, you need a data set which consists of a number of points with x values and y values. Enter this data set in the textbox in the upper right with each point on its own line (no commas or parentheses). For example
1 2 2 3 4 4 5 5 8 10
Next, click the start button. You should see the points plotted on the axes on the left side of the screen. (Note: some points may not scale right on the axes. Just a little bug to be squashed.)
There are two ways to run the least-squares visualizer: in manual mode and in automatic mode.
If you click on the manual tab, you will see two sliders, one for m, the slope of the line and a slider for b, the y-intercept for the line. You can slide each slider to change the features of the line. Each point is plotted as a black dot and the square of each residual is plotted as a square (in light red) that connects the dot and the blue line.
There is also a value of E2 which is the sum of the squares of the residual (the area of the boxes). The goal of find the best least-square (or regression) line is to find the m and b that minimizes the value of E2.
To switch to this mode, click on the "auto" tab on the right side of the screen. This mode finds the values of m and b that minimizes E2. Click on the button "Find the least-squares line" and up will pop m, b and E2. Also a purple line will appear on the plot with the given slope and intercept.