SCATTER PLOTS & LINES OF BEST FIT

What is a scatter plot? A graph that shows the relationship between 2 variables. A line of best fit shows the TREND of that relationship

Making a Prediction When Given a Scatter Plot

Constructing your Own Scatter Plot Step 1 – Identifying your variables INDEPENDENT VARIABLE (x) - can be controlled or manipulated DEPENDENT VARIABLE (y) - Cannot be controlled, viewed as the result of the independent variable

DETERMINING THE INDEPENDENT AND DEPENDENT VARIABLES Independent (x) - horizontal Dependent (y) -vertical Amount you eat Hours studying Advertising Speed Alcohol Consumption Smoking Weight (+ -) Test Scores Sales Time (-) Coordination (-) Lung Cancer

Scatter Plot – A plot of the data points Draw a scatter plot: # of absences (x) Final grade (y) 6 82 2 86 15 43 9 74 12 58 5 90 8 78 Choose an appropriate scaling for each variable. X’s – by 2’s Y’s – by 20’s Then plot your points! Label your axes!

Grade in Class vs. Number of Absences Final Grade Number of Absences

Draw the line of best fit through the center of your points Grade in Class vs. Number of Absences Draw the line of best fit through the center of your points Final Grade Number of Absences

Analyzing the scatter plot This is called a NEGATIVE CORRELATION (as absences go UP, grades go DOWN) Notice the line of best fit has a negative slope!

Analyzing the scatter plot What is an approximate value for the slope of the line of best fit? What does it represent in this problem? Find 2 points on the line of best fit: (5, 98) & (12, 58) Find the slope: (90-58)/(5-12) = 32/-7 = -4.57 points/absence Your grade drops approximately 4.57 points per every absence

Example 2 The following data set represents the number of years a student studied German and the grade they received on a proficiency test on that language. Draw a scatter plot for the data. Draw a line of best fit through (5,89) and (3,63) Predict a score on the test for someone with only 1 year of schooling Number of Years Grade on Test 3 57 4 78 72 2 58 5 89 63 73 84 75 48

Grade on Proficiency Test vs. years studying German on Test Number of Years

Using a Break on an Axis for More Accurate Scaling

Scatter Plot Showing No Correlation

Finding an equation of the line of best fit Let’s look back at our line from the German Proficiency Test What do we know about this line? (It passes through the points (5,89) and (3,63)) It must be in the form y = mx + b How can we find “m” and “b’? Find m! Find b!

Finding an equation of a line of best fit The table below shows the price of a half-gallon of milk from 2000 to 2006. It is known that there is a positive correlation for this data set. Find the line of best fit that corresponds to the years 2002 and 2004 Find m! Year 2000 2001 2002 2003 2004 2005 2006 Cost ($) 1.87 1.89 1.90 1.93 1.94 1.98