1. CHAPTER 10 & 13 Correlation and Regression
Instructor: Alaa saud
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2. Correlation Coefficient :
Correlation :is a statistical method used to determine whether a linear relationship between 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?
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3. 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.
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4. Note: This PowerPoint is only a summary and your main source should be the book.

5. 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.
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6. 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.
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7. 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

8. r = 0.982 (strong positive relationship)
Solution :
r = 0.982
r = (strong positive relationship)
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9. 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
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10. r = -0.944 (strong negative relationship)
Solution :
r = (strong negative relationship)
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11. The formula for the Spearman Rank correlation coefficient
Where :
d=difference in rank
n=number of data pairs
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12. 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
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13. 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
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14. 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
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15. 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
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16. rs = 0.643 (strong positive relationship)
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