1. Warm Up
Scatter Plot Activity

2. Bivariate Data – Scatter Plots and Correlation Coefficient

3. Objective
Construct Scatter Plots and find Correlation Coefficient using Formula

4. Relevance
To be able to graphically represent two quantitative variables and analyze the strength of the relationship.

5. 2 Quantitative Variables……
We represent 2 variables that are quantitative by using a scatter plot.
Scatter Plot – a plot of ordered pairs (x,y) of bivariate data on a coordinate axis system. It is a visual or pictoral way to describe the nature of the relationship between 2 variables.

6. Input and Output Variables……X:
a. Input Variable
b. Independent Var
c. Controlled Var Y:
a. Output Variable
b. Dependent Var
c. Results from the Controlled variable

7. Example
When dealing with height and weight, which variable would you use as the input variable and why?
Answer:
Height would be used as the input variable because weight is often predicted based on a person’s height.
Normal acceptable weight ranges are based on a person’s height!

8. Constructing a scatter plot
Do a scatter plot of the following data:
Independent
Dependent
Variable
Age
Blood Pressure 43
128 48
120 56
135 61
143 67
141 70
152

9. What do we look for?
A. Is it a positive correlation, negative correlation, or no correlation?
B. Is it a strong or weak correlation?
C. What is the shape of the graph?

10. Answer using GDC Age Blood Pressure 43 128 48 120 56 135 61 143 67 14170
152

11. Notice Notice the following:
A. Strong Positive – as x increases, y also increases.
B. Linear - it is a graph of a line.

12. Example 2 – NO GDC Independent Dependent Variable # of Absences
# of Absences
Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78

13. Example 2 using GDC Independent Dependent Variable # of Absences
# of Absences
Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78

14. Notice Notice the following:
Strong Negative – As x increases, y decreases
Linear – it’s the graph of a line.

15. Example 3 – NO GDC Independent Dependent Variable Hrs. of Exercise
Hrs. of Exercise
Amt of Milk 3 48 8 2 32 5 64 10 56 72 1

16. Example 3 using GDC Independent Dependent Variable Hrs. of Exercise
Hrs. of Exercise
Amt of Milk 3 48 8 2 32 5 64 10 56 72 1

17. Notice
Notice:
There seems to be no correlation between the hours or exercise a person performs and the amount of milk they drink.

18. Steps for Scatter Plot using GDC
Put x’s in L1 and y’s in L2
Click on “2nd y=“
Set scatter plot to look like the screen to the right.
Press zoom 9 or set your own window and then press graph.

19. Linear Correlation

20. Correlation
Definition – a statistical method used to determine whether a relationship exists between variables.
3 Types of Correlation:
A. Positive
B. Negative
C. No Correlation

21. Positive Correlation: as x increases, y increases or as x decreases, y decreases.
Negative Correlation: as x increases, y decreases.
No Correlation: there is no relationship between the variables.

22. Linear Correlation Analysis
Primary Purpose: to measure the strength of the relationship between the variables.
*This is a test question!!!!

23. Coefficient of Linear Correlation
The numerical measure of the strength and the direction between 2 variables.
This number is called the correlation coefficient.
The symbol used to represent the correlation coefficient is “r.”

24. The range of “r” values
The range of the correlation coefficient is -1 to +1.
The closer to 0 you get, the weaker the correlation.

25. Range ____________________________________ -1 0 +1 Strong
Negative No Linear Relationship Strong
Positive
____________________________________

26. Computational Formula using z-scores of x and y

27. Example 1
Find the correlation coefficient (r) of the following example.
Use the lists in the calculator. x y 2 80 5 1 70 4 90 60

28. Find mean and standard deviation first
Since you will be using a formula that uses z-scores, you will need to know the mean and standard deviation of the x and y values.
Put x’s in L1
Put y’s in L2
Run stat calc one var stats L1 – Write down mean & st. dev.
Run stat calc one var stats L2 – Write down mean & st. dev.
Better Option: 2nd Stat Math
Mean (L?)
Store It!!!!!

29. Shown on GDC – Write Down
x values:
y values:

30. Calculator Lists Set Formula L1 L2 L3 = (L1-2.8)/1.643167673
L5 = L3 x L4 x y
z(of x)
z (of y)
z (of x) times z(of y) 2 80 5
1.3389 1 70
-1.095 4 90
0.7303
1.2279 60
-1.403

31. Calculate “r”
From the lists…..
n = 5

32. What does that mean?
Since r = 0.61, the correlation is a moderate correlation.
Do we want to make predictions from this?
It depends on how precise the answer needs to be.

33. Example 2 Find the correlation coefficient (r) for the following data.
Do you remember what we found from the scatter plot?
Age
Blood Pressure 43
128 48
120 56
135 61
143 67
141 70
152

34. Let’s do this one together
Remember to use your lists in the calculator.
Don’t round numbers until your final answer.
Find the mean and st. dev. for x and y.
Explain what you found.

35. X Values:
Y Values:

36. List values you should have43
128
-1.368
1.0205 48
120
-1.448
1.2978
n=6 56
135 61
143 67
141 70
152
1.1796
1.36
1.6042

37. Compute “r”

38. Describe it
Since r = 0.897
Strong Positive Correlation

39. Example 3…… Find the correlation coefficient for the following data.
Do you remember what we found from the scatter plot?
# of Absences
Final Grade 6 82 2 86 15 43 9 74 12 58 5 90 8 78

40. X Values:
Y Values:

41. List Values using GDC L1 L2 L3 L4 L5 6 82 -0.4898 0.53626 -0.2626 2 86
-1.404
0.7746
-1.088 15 43
1.5673
-1.788
-2.802
n=7 9 74 12 58 5 90
1.0129 8 78

42. Compute “r”

43. Describe it
Since r =
Strong Negative Correlation

44. Example 4 Find the correlation coefficient of the following data.
Do you remember what we found from the scatter plot?
Hrs of Exercise
Amt of Milk 3 48 8 2 32 5 64 10 56 72 1

45. x Values:
y Values:

46. List Values using GDC Hrs of Exercise Amt of Milk L3 L4 L5 3 48 8
-1.206
-1.476
1.7804 2 32
-0.603 5 64
1.0205
n=9 10
1.206
-1.387
-1.673 56
1.8091
1.2008 72
1.3771 1

47. Compute “r”

48. Describe It
Since r = .067
No Correlation…..No correlation exists

49. What is It is the coefficient of determination.
It is the percentage of the total variation in y which can be explained by the relationship between x and y.
A way to think of it: The value tells you how much your ability to predict is improved by using the regression line compared with NOT using the regression line.

50. For Example
If it means that 89% of the variation in y can be explained by the relationship between x and y.
It is a good fit.

51. Assignment
Worksheet