Applying linear and median regression Lab 8 Applying linear and median regression

Graphing calculators can be used to calculate and plot a line of best fit using linear regression Use the data on p. 323 Calculate and plot linear regression from the table Practice p. 324 a

Finding the line of best fit Lesson 45 Finding the line of best fit

regression Regression is the process of identifying a relationship between variables. A measure of the strength and direction of the relationship between 2 variables or data sets is called correlation

Linear correlation When the points tend to gather about a line, there is a linear relationship, or linear correlation. A scatter plot of the points will indicate whether there is a positive correlation (points rise from left to right) or a negative correlation (points fall from left to right) When the points are widely scattered, there will be little or no correlation

Line of best fit A line that best fits the points in a scatter plot is a line of best fit ( or regression line) A line of best fit will have about the same number of points above and below it. It may or may not go through one or more of the points on the graph

Describing correlation and estimating a line of best fit Create a scatter plot of the following data: # of people in house 1 2 3 4 5 6 Aver. mail per day 4 6 6 9 8 6 Plot points (people,mail) Since the points rise from left to right , there is a positive correlation. Sketch the line of best fit Use 2 points to find the slope and point-slope form to write an equation of the line

Correlation coefficient The strength and direction of a linear correlation is measured by the correlation coefficient, r. Values of r can range from -1 to 1, where negative values indicate negative correlation and positive values indicate positive correlation. The further r is from 0, the closer the points are to a straight line When there is no correlation, r = 0

Estimating the r value Once you create a scatter plot, you can estimate the r value by remembering that the closer the points are to a straight line the closer the correlation is to -1 or 1

Using the graphing calculator Enter data into L1 and L2 Be sure you go to CATALOG and scroll down to DIAGNOSTICSON and press ENTER twice Follow directions as in lab 8 The r is the correlation.

Collecting and analyzing data Step 1: 1 student bounces a tennis ball and one student times how long it takes for the ball to stop bouncing, while the other students count the number of times the ball bounces during that time. Do this 10 times. Step 2: record the number of seconds that ball bounces and number of bounces. Step 3: plot points, sketch line of best fit, find equation of line, and estimate the correlation coefficient