Scatter Diagrams Objective Draw and interpret scatter diagrams

Scatter Diagrams Objective: Draw and interpret scatter diagrams. Distinguish between linear and nonlinear relations. Use a graphing utility to find the line of best fit.

Terms n Relation n Correspondence between two sets n Dependent variable : y the value of y is determined by the value of x n Independent variable : x n Scatter diagram Plot the ordered pairs using rectangular coordinates.

Linear data n To determine if data is linear n Graph the data n Does the data have a general pattern of increasing or decreasing? n Look on page 201: can you see the “linear” pattern in those graphs stated as being linear? Do you see that those marked “nonlinear” do not have this pattern?

Finding a Linear Regression (Line of Best Fit) Graph the data 2. Draw a line through the data 3. Identify two points on the line drawn through the data. (These points may or may not be data points. ) 4. Find the equation of the line using the points selected. 1. 2. 3. Find slope Find y-intercept Write equation

Using a calculator n n n n n Go to STAT mode Select EDIT Clear old data Input new data Quit Go back to STAT mode Select CALC Select Lin. R The calculator will give you the slope and yintercept. Use these values to write the equation.

n Know your calculator n a: slope or y-intercept depending on the calculator n b: slope or y-intercept depending on the calculator n corr: value showing how well the equation describes the data -1: perfect linear pattern going down 1: perfect linear pattern going up 0: no linear pattern Closer the “correlation coefficient” is to -1 or 1 the better the fit of the line. n n: number of data values inputted into calculator

Assignment n Page 204 n #5, 7, 9, 13, 15, 17, 19