advanced math topics 11.1-11.3 the coefficient of correlation
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Advanced Math Topics
11.1-11.3 The Coefficient
Of Correlation
Is there a correlation between the two variables?
What would the graph look like?
Is this a positive, negative, or no correlation?
Age
Blood Pressure
Weight of a Vehicle
Mileage
I.Q.
BowlingScore
Positive CorrelationNegative Correlation
.
.
.
.
..
.
.
.No Correlation
The Coefficient of Linear Correlation
2222 )()()()(
))(()(
yynxxn
yxxynr
The result will always be between -1 and +1, inclusive. A value of +1 means perfect positive correlation (all points are on one line).A value of -1 means perfect negative correlation (all points are on one line).A value of 0 means there is no correlation between the two variables.
1) Create a scatter plot and find the coefficient of correlation of the following:
Math Scores:
Business Scores:
52
48
49
49
26
27
28
24
63
59
44
40
70
72
32
31
49
50
51
49
Use graph paper or the lines on your binder paper and a ruler to create an organized scatter plot.
Math Scores
BusinessScores
20
30 40 50 60 70 80
30
40
50
60
70
80
20
..
..
.
.
.
.
..There seems to be a highpositive correlation.
1) Create a scatter plot and find the coefficient of correlation of the following:
Math Scores:
Business Scores:
52
48
49
49
26
27
28
24
63
59
44
40
70
72
32
31
49
50
51
49
2222 )()()()(
))(()(
yynxxn
yxxynr
n
xy
y
x
y
x
2
2
769,19664,18
954,18r
464
449
23,396
22,137
22,729
10
r = 0.9867Round to the nearest ten-thousandth.
From the HW: P. 545-546 2) Create a scatter plot and find the coefficient of correlation of the following:
Height, x:
Shoe size, y:
65
7.5
67
8.5
67
8
71
10
72
11
r = 0.9828
HW: P. 545-546 #1-5