9.2 Video Notes:

Lines of Fit

Learning Objective: Draw the line of fit for a scatter plot and analyze the equation of the line.

A line of fit is a line drawn on a scatter plot close to most of the data points.  It can be used to estimate data on a graph.

Example 1: The table shows the depth of a river x months after a monsoon season ends.                                                                                                        

a) Make a scatter plot of the data and draw a line of fit.

b) Write an equation of the line of fit.

c) Interpret the slope and the y-intercept of the line of fit.

d) Predict the depth in month 9

Graphing calculators use a method called linear regression to find a precise line of fit called a line of best fit.  This line best models a set of data.

A calculator often gives a value r called the correlation coefficient.  This value tells whether the correlation is positive or negative, and how closely the equation models the data.  Values of r range from -1 to 1.  When r is close to 1 or -1, there is a strong correlation between the variables.  As r gets closer to 0, the correlation becomes weaker.

9.2 Practice Problem

The table shows the numbers of people who have attended a festival over an 8-year period.  

a) Make a scatter plot of the data and draw a line of fit.

b) Write an equation of the line of fit.

c) Interpret the slope and the y-intercept of the line of fit.

d) Predict the number of people who will attend the festival in year 10.