How To Write A Prediction Equation For A Scatter Plot

A scatter plot features points spread across a graph's axes. The points do not fall upon a single line, so no single mathematical equation can define all of them. Yet you can create a prediction equation that determines each point's coordinates. This equation is the function of the line of best fit through the plot's many points. Depending on the strength of the correlation between the graph's variables, this line may be very steep or close to horizontal.

Step 1

Draw a shape around all the points on the scatter plot. This shape should appear significantly longer than it is wide.

Step 2

Mark a line through this shape, creating two equally sized shapes that are also longer than they are wide. An equal number of scatter points should appear on either side of this line.

Step 3

Choose two points on the line you have drawn. For this example, imagine that these two points have coordinates of (1,11) and (4,13).

Step 4

Divide the difference between these points' y-coordinates by the difference in their x-coordinates. Continuing this example: (11 – 13) ÷ (1 – 4) = 0.667. This value represents the slope of the line of best fit.

Step 5

Subtract the product of this slope and a point's x-coordinate from the point's y-coordinate. Applying this to the point (4,13): 13 – (0.667 × 4) = 10.33. This is the intercept of the line with the y-axis.

Step 6

Substitute the line's slope and intercept as "m" and "c" in the equation "y = mx + c." With this example, this produces the equation "y = 0.667x + 10.33." This equation predicts the y-value of any point on the plot from its x-value.