Lines of Best Fit When data show a correlation, you can estimate and draw a line of best fit that approximates a trend for a set of data and use it to make predictions. Line of Best Fit: a straight line that comes closest to the points on a scatter plot. Steps for Drawing the Line of Best Fit: 1.) Plot the data as ordered pairs – make a scatter plot. 2.) Study the points to see if there is a relationship between the 2 sets of data – positive, negative, or no association (see Data Relationships slide).

Data Relationships There are three ways to describe data displayed in a scatter plot and the adjectives “strong” and “weak” can also be used to further define the association. Positive Association Negative Association No Association The values in both data sets increase or decrease at the same time. The values in one data set increase as the values in the other set decrease. The values in both data sets show no pattern.

Steps for Drawing a Line of Best Fit (cont.): 3.) Draw a line of best fit. It should be as close as possible to most of the points – look for the center – and go in the same direction as the points. Try to draw the line so that about the same number of points are above the line as below the line. Draw the line so that it goes through some corners where the grid lines meet (integers) to help you write the equation of the line of best fit in slope-intercept form (y=mx+b).

Writing an Equation for the Line of Best Fit Once you’ve drawn a line of best fit, you can find the slope, y-intercept, and write the equation of the line – just like with any linear function. Slope: Pick 2 points on the line where it meets the corners where the x & y grid lines intersect (to get integers). Then use the slope formula/L method. Y-intercept: Use slope and one point (x,y) in the slope-intercept form (y=mx+b) and solve for b. To estimate b, look at where the line crosses the y-axis. Equation: Write in slope-intercept form: y = mx + b using the m and b values you calculated.

Example 1 – Data & Line of Best Fit

Example 2 – Data & Line of Best Fit

Example 3 – Data & Line of Best Fit Years since 1990 weight (lb) 100 120 140 160 180 2 4 6 8 10 200

Which graph shows the line of best fit? Why? D.