7-2 Correlation Coefficient Objectives Determine and interpret the correlation coefficient.
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7-2 Correlation Coefficient
Objectives
• Determine and interpret the correlation coefficient.
Correlation Coefficient - Facts
• Correlation coefficient is always between -1 and +1.– Weak correlation is closer to zero and strong correlation
is closer to either -1 or +1.• Ex. r = 0.21 or -0.21 (weak), r = -0.98 or 0.98(strong).
– If correlation is equal to exactly -1 or +1 then the data points all fall on an exact straight line.
r = +.3 r = +1
Examples of Approximate r Values
y
x
y
x
y
x
y
x
y
x
r = -1 r = -.6 r = 0
0
20
40
60
80
100
120
140
40 60 80 100 120 140
r =1
1. Estimate the correlation coefficient (r-value).
0
20
40
60
80
100
120
140
40 60 80 100 120 140
1. Estimate the correlation coefficient (r-value).
0
20
40
60
80
100
120
140
40 60 80 100 120 140
2. Estimate the correlation coefficient (r-value).
r =-1
0
20
40
60
80
100
120
140
40 60 80 100 120 140
3. Estimate the correlation coefficient (r-value).
0
20
40
60
80
100
120
140
40 60 80 100 120 140
3. Estimate the correlation coefficient (r-value).
r = 0.95
0
20
40
60
80
100
120
140
40 60 80 100 120 140
4. Estimate the correlation coefficient (r-value).
r =-0.95
0
20
40
60
80
100
120
140
160
40 60 80 100 120 140
5. Estimate the correlation coefficient (r-value).
0
20
40
60
80
100
120
140
160
40 60 80 100 120 140
5. Estimate the correlation coefficient (r-value).
r = 0.6
0
20
40
60
80
100
120
140
40 60 80 100 120 140
6. Estimate the correlation coefficient (r-value).
r = -0.6
Correlation Coefficient
7. Estimate the correlation coefficient (r-value).
r = 0.9
Correlation Coefficient
7. Estimate the correlation coefficient (r-value).
Correlation Coefficient
8. Estimate the correlation coefficient (r-value).
Correlation Coefficient
8. Estimate the correlation coefficient (r-value).
r = 0.4
Correlation Coefficient
9. Estimate the correlation coefficient (r-value).
Correlation Coefficient
9. Estimate the correlation coefficient (r-value).
r = 0
10. a) draw a scatter plot of the data
b) draw in the best fit line
X 15 25 35 45 55Y 41 36 35 33 30
15 20 25 30 35 40 45 50 55 60 65 70
30
3
2
3
4
3
6 3
8
4
0
10. a) draw a scatter plot of the data
b) draw in the best fit line
X 15 25 35 45 55Y 41 36 35 33 30
15 20 25 30 35 40 45 50 55 60 65 70
30
3
2
3
4
3
6 3
8
4
0
10. c) find the equation of your best fit line
15 20 25 30 35 40 45 50 55 60 65 70
30
3
2 3
4
3
6
3
8
40
4
2
4
4
1 45 50 55 0 5 10
Y-intercept
45
-4
15Slope
4
15
445
15y x
10. d) estimate y when x = 20
15 20 25 30 35 40 45 50 55 60 65 70
30
3
2 3
4
3
6
3
8
40
4
2
4
4
1 45 50 55 0 5 10
About 40
11. Find the correlation Coefficient
X 15 25 35 45 55Y 41 36 35 33 30
15 20 25 30 35 40 45 50 55 60 65 70
30
3
2
3
4 3
6
38
4
0
Classwork/Homework
7-2 Worksheet
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