1. SCATTER PLOTS & LINES OF BEST FIT

2. 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

3. Making a Prediction When Given a Scatter Plot

4. 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

5. 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

6. 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!

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

8. 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

9. 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!

10. 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 = points/absence
Your grade drops approximately 4.57 points per every absence

11. 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

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

13. Using a Break on an Axis for More Accurate Scaling

14. Scatter Plot Showing No Correlation

15. 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!

16. Finding an equation of a line of best fit
The table below shows the price of a half-gallon of milk from 2000 to 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