Scatter Diagrams; Linear Curve Fitting Objectives: Draw and Interpret Scatter Diagrams Distinguish between Linear and Nonlinear Relations Use a Graphing Utility to Find the Line of Best Fit

Scatter Diagrams  A relation is a correspondence between two sets. Often we are interested in specifying the type of relation (such as an equation) that might exist between two variables. The first step in finding this relation is to plot the ordered pairs using rectangular coordinates. The resulting graph is called a scatter diagram.

EX 1: Find the equation of the line by hand XY a)Draw a scatter diagram by hand b)Select two points from the scatter diagram c)Find the equation of the line containing the points selected

Mortgage Qualification: The amount of money that a lending institution will allow you to borrow mainly depends on the interest rate and your annual income. The following data represent the annual income I required by a bank in order to lend L dollars at an interest rate of 7.5% for 30 years Annual Income Loan Amount 15,00044,600 20,00059,500 25,00074,500 30,00089,400 35,000104,300 40,000119,200 45,000134,100 50,000149,000 55,000153,900 60,000178,800 65,000193,700 70,000208,600 a)Use a graphing utility to draw a scatter diagram of the data b)Use a graphing utility to find the line of best fit to the data c)Graph the line of best fit on the scatter diagram d)Interpret the slope of the line of best fit d)Determine the loan amount that an individual would qualify for if her income is $42,000