1. CHAPTER 10 & 13 Correlation and Regression
Instructor: Alaa saud
Note: This PowerPoint is only a summary and your main source should be the book.

2. Outline: Introduction 10-1 Scatter plots 10-2 Correlation .
10-3 Correlation Coefficient .
10-4 Regression .

3. The purpose of this chapter is to answer these questions statistically:
1. Are two or more variables related?
2. If so, what is the strength of the relationship?
3. What type of relationship exists?
4. What kind of predictions can be made from the relationship?
Note: This PowerPoint is only a summary and your main source should be the book.

4. Correlation and Regression are inferential statistics involves determining whether a relationship between two or more numerical or quantitative variables exists.
Examples:
Is the number of hours a student studies is related to the student’s score on a particular exam?
Is caffeine related to heart damage?
Is there a relationship between a person’s age and his or her blood pressure?

5. Introduction
Correlation is a statistical method used to determine whether a linear relationship between variables exists.
Regression is a statistical method used to describe the nature of the relationship between variables that is, positive or negative, linear or nonlinear.

6. simple multiple There are two types of relationships
In a simple relationship, there are two variables: an
independent variable (predictor variable)
dependent variable (response variable).
In a multiple relationship, there are two or more independent variables that are used to predict one dependent variable.
Note: This PowerPoint is only a summary and your main source should be the book.

7. Simple relationship can also be positive or negative.
Positive relationship exists when both variables increase or decrease at the same time.
Example: a person’s height and perfect weight.
Negative relationship, as one variable increases, the other variable decreases and vice versa.
Example: the strength of people over 60 years of age.

8. Example: The type of relationship: The independent variable(s):
Is there a relationship between a person’s age and his or her blood pressure?
The type of relationship:
The independent variable(s):
The dependent variable:

9. Example:
Is there a relationship between a students final score in math and factors such as the number of hours a student studies, the number of absences, and the IQ score.
The type of relationship:
The independent variable(s):
The dependent variable:

10. Predictions are made in all areas and daily. Examples:
include weather forecasting, stock market analyses, sales predictions, crop predictions, gasoline price predictions, and sports predictions. Some predictions are more accurate than others, due to the strength of the relationship. That is, the stronger the relationship is between variables, the more accurate the prediction is.
Note: This PowerPoint is only a summary and your main source should be the book.

11. Scatter Plots
Note: This PowerPoint is only a summary and your main source should be the book.

12. Types of relationships:
A scatter plot :is a graph of the ordered pairs (x, y) of numbers consisting of the independent variable x and the dependent variable y.
Types of relationships:
Positive linear relationship
Negative linear relationship
Curvilinear or nonlinear relationship
No Relation

13. Strength of relationships:
Positive strong
Positive perfect
Positive Weak
Negative perfect
Negative strong
Negative Weak
Note: This PowerPoint is only a summary and your main source should be the book.

14. Example 10-1:
Construct a scatter plot for the data shown for car rental companies in the United States for a recent year.
Solution :
Step 1: Draw and label the x and y axes.
Step 2: Plot each point on the graph.
Note: This PowerPoint is only a summary and your main source should be the book.

15. Independent
Dependent
Note: This PowerPoint is only a summary and your main source should be the book.

16. Example 10-2:
Construct a scatter plot for the data obtained in a study on the number of absences and the final grades of seven randomly selected students from a statistics class.
Student
Number of absences x
Final grade y A 6 82 B 2 86 C 15 43 D 9 74 E 12 58 F 5 90 G 8 78
Note: This PowerPoint is only a summary and your main source should be the book.

17. Y X
Note: This PowerPoint is only a summary and your main source should be the book.

18. Example 10-3:
A researcher wishes to see if there is arelationship between the ages of the wealthiest people in the world and their net worth. A random sample of 10 persons was selected.
Person
Age x
Net worth y A 60 11 B 72 69 C 56
11.9 D 55 30 E 83
12.2 F 67 36 G 38
18.7 H 62
10.2 I
23.3 J 46
10.6
Note: This PowerPoint is only a summary and your main source should be the book.

20. Correlation Coefficient
Note: This PowerPoint is only a summary and your main source should be the book.

21. The population coefficient denoted by ρ is the correlation computed by using all possible pairs of data values taken from a population.
The correlation coefficient computed from the sample data measures the strength and direction of a linear relationship between two variables.

22. The range of the correlation coefficient is
from 1 to 1.
If there is a strong positive linear relationship between the variables, the value of r will be close to 1.
If there is a strong negative linear relationship between the variables, the value of r will be close to 1.

23. Note: This PowerPoint is only a summary and your main source should be the book.

24. Correlation Coefficient
Pearson
Ch (10)
Spearman Rank
Ch (13)
-Denoted by ( r )
-Only Used when Two
variables are quantitative.
-Denoted by ( rs)
-Used when Two
variables are Quantitative
or Qualitative.

25. 1- Pearson correlation coefficient
There are several types of correlation coefficients. The one explained in this section is called the Pearson product moment correlation coefficient (PPMC).
The symbol for the sample correlation coefficient is r. The symbol for the population correlation coefficient is .

26. where n is the number of data pairs.
The formula for the Pearson correlation coefficient is
where n is the number of data pairs.
Rounding Rule: Round to three decimal places.
Note: This PowerPoint is only a summary and your main source should be the book.

27. Example 10-4:
Compute the correlation coefficient for the data in Example 10–1.
company
Cars x
Income y A
63.0
7.0 B
29.0
3.9 C
20.8
2.1 D
19.1
2.8 E
13.4
1.4 F
8.5
1.5 xy x2 y2
441
3969 49
113.10
841
15.21
43.68
432.64
4.41
53.48
364.81
7.84
18.76
179.56
1.96
2.75
72.25
2.25
Σx =
153.8
Σy =
18.7
Σxy =
682.77
Σx2 =
Σy2 =
80.67

28. r = 0.982 (strong positive relationship)
Solution :
r = 0.982
r = (strong positive relationship)
Note: This PowerPoint is only a summary and your main source should be the book.

29. Example 10-5:
Compute the correlation coefficient for the data in Example 10–2.
company
No. of absence
grade A 6 82 B 2 86 C 15 43 D 9 74 E 12 58 F 5 90 G 8 78 xy x2 y2
492 36
6.724
172 4
7.396
645
225
1.849
666 81
5.476
696
144
3.364
450 25
8.100
624 64
6.084
Σx = 57
Σy = 511
Σxy =
3745
Σx2 =
579
Σy2 =
38.993
Note: This PowerPoint is only a summary and your main source should be the book.

30. r = -0.944 (strong negative relationship)
Solution :
r = (strong negative relationship)
Note: This PowerPoint is only a summary and your main source should be the book.

31. 2- Spearman Rank correlation coefficient
Other types of correlation coefficients. Is called the Spearman rank correlation coefficient, can be used when the data are ranked.
The formula for the correlation coefficient is
Where
d = difference in ranks.
n = number of data pairs.

32. Example (13-7):
Two student were asked to rate eight different textbook for a specific course on an ascending scale from 0 to 20 points .Points were assigned for each of several categories, such as reading level ,use of illustration .
Textbook
Student 1’s rating
Student 2’s rating A 4 B 10 6 C 18 20 D 14 E 12 16 F 2 8 G 5 11 H 9 7
Note: This PowerPoint is only a summary and your main source should be the book.

33. Solution :
Student 1’s rating 4 10 18 20 12 2 5 9
Student 1’s rating 20 18 12 10 9 5 4 2 1 2 3
Rank 4 5 6 7 8
Note: This PowerPoint is only a summary and your main source should be the book.

34. Student 2’s rating 4 6 20 14 16 8 11 7
Student 2’s rating 20 16 14 11 8 7 6 4 1 2
Rank 3 4 5 6 7 8
Note: This PowerPoint is only a summary and your main source should be the book.

35. Textbook
Student 1’s rating A 4 B 10 C 18 D 20 E 12 F 2 G 5 H 9 X1 7 4 2 1 3 8 6 5
Student 2’s rating 4 6 20 14 16 8 11 7 X2 8 7 1 3 2 5 4 6
d=x1-x2 -1 -3 1 -2 3 2 1 9 4
Note: This PowerPoint is only a summary and your main source should be the book.

36. rs = 0.643 (strong positive relationship)
Note: This PowerPoint is only a summary and your main source should be the book.