A **line of best fit ** is a straight line that is the best approximation of the given set of data.

It is used to study the nature of the relation between two variables.

A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

A more accurate way of finding the line of best fit is the **least square method **.

Use the following steps to find the equation of line of best fit for a set of ordered pairs.

Step 1: Calculate the mean of the *x*-values and the mean of the *y*-values.

Step 2: Compute the sum of the squares of the *x*-values.

Step 3: Compute the sum of each *x*-value multiplied by its corresponding *y*-value.

Step 4: Calculate the slope of the line using the formula:

where

nis the total number of data points.

Step 5: Compute the *y*-intercept of the line by using the formula:

where are the mean of the

x- andy-coordinates of the data points respectively.

Step 6: Use the slope and the *y *-intercept to form the equation of the line.

**Example:**

Use the least square method to determine the equation of line of best fit for the data. Then plot the line.

**Solution:**

Plot the points on a coordinate plane.

Calculate the means of the *x*-values and the *y*-values, the sum of squares of the *x*-values, and the sum of each *x*-value multiplied by its corresponding *y*-value.

Calculate the slope.

Calculate the *y*-intercept.

First, calculate the mean of the *x*-values and that of the *y*-values.

Use the formula to compute the *y*-intercept.

Use the slope and *y*-intercept to form the equation of the line of best fit.

The slope of the line is –1.1 and the *y *-intercept is 14.0.

Therefore, the equation is *y * = –1.1 *x * + 14.0.

Draw the line on the scatter plot.