1. Scatter Plots
and
Correlations
Dittamo Lewis Notes 2013

2. Scatter Plots
A Scatter Plot is a picture of numerical data in which each point (x,y) is located on a rectangular coordinate plane.
The horizontal axis is identified with values of x and the vertical axis with values of y.
Dittamo Lewis Notes 2013

3. A Scatter Plot is the graph of ordered pairs (x,y)
Scatter Plots
A Scatter Plot is the graph of
ordered pairs (x,y)
Correlation
A Correlation is a relationship between points.
Dittamo Lewis Notes 2013

4. (x, y) (1,4) (3,2) (2,5) (4,6) (7,9) (6,8) (5,7) Scatter Plots
Look at this Scatter Plot
Dittamo Lewis Notes 2013

5. (x, y) (1,4) (3,6) (2,1) (4,3) (7,2) (6,4) (5,1) Scatter Plots
Look at this Scatter Plot
(x, y)
(1,4)
(3,6)
(2,1)
(4,3)
(7,2)
(6,4)
(5,1)
Dittamo Lewis Notes 2013

6. Scatter Plots
Any comments on these two graphs? Is there anything special about them?
Looking at a scatter plot can sometimes allow us to determine if a relationship exists between two variables.
If all of the points are close to forming a line there could be a relationship.
Dittamo Lewis Notes 2013

7. Scatter Plots
Brain
Weight (g)
Max.
Life (yr.)
Animal y
Mouse
0.4
3.2 50 40 30 20 10
Fox
50.4
9.8
Tiger
157
22.4
Max. Life (yrs.)
Sheep
175 20
Pig
180 27
Seal
325 41 x
Donkey
419 40
Brain Weight (g)
Monkey
440 50
Dittamo Lewis Notes 2013

8. Scatter Plots Scatterplot - a coordinate graph of data points.y 50 40 30 20 10
Trend is increasing
Trend looks linear
Max. Life (yrs.)
Line of Best Fit
-Points act like
magnets attracting
the line. x
Brain Weight (g)
Dittamo Lewis Notes 2013

9. Scatter Plots Scatterplot - a coordinate graph of data points.y 50 40 30 20 10
Trend is increasing
Trend looks linear
Max. Life (yrs.)
Line of Best Fit
-Points act like
magnets attracting
the line. x
Brain Weight (g)
Dittamo Lewis Notes 2013

10. Scatter Plots Scatterplot - a coordinate graph of data points.y 50 40 30 20 10
Trend is increasing
Trend looks linear
Max. Life (yrs.)
Line of Best Fit
-Points act like
magnets attracting
the line. x
Brain Weight (g)
Dittamo Lewis Notes 2013

11. Scatter Plots Scatterplot - a coordinate graph of data points.y 50 40 30 20 10
Trend is increasing
Trend looks linear
Max. Life (yrs.)
Line of Best Fit
-Points act like
magnets attracting
the line. x
Brain Weight (g)
Dittamo Lewis Notes 2013

12. Which scatterplots below show a linear trend?1) 2) 3)
Negative
Correlation
Positive
Correlation
Dittamo Lewis Notes 2013

13. Which scatterplots below show a linear trend?1) 2) 3)
Constant
Correlation
Dittamo Lewis Notes 2013

14. Scatter Plots
The independent variable is on the x-axis and the dependent variable is on the y-axis.
Dependent
Variable
(Y)
Independent Variable (X)
Dittamo Lewis Notes 2013

15. Scatter Plots
If the x increases and the y increases there is a positive correlation.
Examples:
Father’s height vs. Son’s height
Daily grade vs. Final grade 3 2 1
Dittamo Lewis Notes 2013

16. Scatter Plots
Notice as the Father’s Height increases so does the Son’s Height.
Dittamo Lewis Notes 2013

17. Father’s Height in Inches
Scatter Plots
Notice all of the points center close to a line which shows us a relation-ship also known as a correlation
Son’s Height
in Inches
Father’s Height in Inches
Dittamo Lewis Notes 2013

18. Scatter Plots
Dittamo Lewis Notes 2013

19. Zero Correlation: There appears to be no linear relationship
Scatter Plots
Zero Correlation: There appears to be no linear relationship
Example:
Height vs. IQ score 4 3 2 1
Your height doesn’t determine how smart you are. No obvious correlation.
Dittamo Lewis Notes 2013

20. No Correlation because the points are scattered everywhere.
Scatter Plots
No Correlation because the points are scattered everywhere.
Dittamo Lewis Notes 2013

21. Scatter Plots
Negative Correlation: If the x increases and the y decreases there is a negative correlation.
Examples:
Car weight vs.
Miles per gallon
Days absent vs. Final grade 4 3 2 1
Dittamo Lewis Notes 2013

22. Scatter Plots
TAKE OUT YOUR
STUDY GUIDE
Dittamo Lewis Notes 2013

23. #9 Scatter Plots Height vs. IQ
A Scatter Plot is the graph of ordered pairs (x,y).
A Correlation is a relationship between points.
A ZERO CORRELATION is when there appears to be no linear relationship.
Example:
Height vs. IQ
*Your height doesn’t determine how smart you are. No obvious correlation.
Dittamo Lewis Notes 2013

24. #10
Positive Correlation: If the x increases and the y increases.
Correlation
Negative Correlation: If the x increases and the y decreases.
Negative
Correlation
Positive
Correlation
Examples:
Dad’s height vs. Son’s height
Daily grade vs. Final grade
Examples:
Car weight vs. MPG
Days absent vs. Final grade
Dittamo Lewis Notes 2013

25. Correlations
and
Graphing

26. Correlation
If the x increases and the y increases there is a positive correlation.
Examples:
Father’s height vs. Son’s height
Daily grade vs. Final grade 3 2 1
Dittamo Lewis Notes 2013

27. Correlation
If the x increases and the y decreases there is a negative correlation. 4 3 2 1
Examples:
Car weight vs.
Miles per gallon
Days absent vs. Final grade
Dittamo Lewis Notes 2013

28. A Zero Correlation is when there appears to be no linear relationship
Example:
Height vs. IQ score 4 3 2 1
Your height doesn’t determine how smart you are. No obvious correlation.
Dittamo Lewis Notes 2013

29. I II IV III Graphing Review A point (x,y) 4 QUADRANT GRAPH
1st QUADRANT GRAPH
y-axis y 3 2 1 -1 -2 -3 I II
(-1,2) x
(-2,0)
Origin (0,0)
x-axis
ORDERED PAIR
(3,-1)
NOT in a quadrant
A point (x,y) IV
III
Dittamo Lewis Notes 2013

30. Independent/Dependent Events#?
The independent variable is on the x-axis and the dependent variable is on the y-axis.
Dependent
Variable
(y)
Independent Variable (x)
The dependent event depends on the independent event.