Linear Regression
Line of Best Fit
When given some data that seems to have a linear relationship, it is possible to find an equation that best fits the data. Follow these steps to find the equation:
Step 1. Plot the ordered pairs and determine if the relationship between the x and y values looks linear.
Step 2. Draw a line that seems to best fit the data.
When drawing in a line, keep these guidelines in mind:
- Have as many points below the line as above the line whenever possible.
- Be sure the line is going in the same direction as the points. One way to check the direction is by drawing in the smallest rectangle possible around the points. The slope of the line should follow the same direction.
- If possible, a point or points should be on the line but the above guidelines are more important.
Step 3. Use two points and find the slope of the line. Use the slope formula m = 
.
Step 4. Estimate the y-intercept or use a point and the slope found in Step 3 to write the equation. Substitute the slope (m) and the point (x1 , y1) into the point-slope form of an equation y - y1 = m (x - x1).