2. A chemical company, wishing to study the effect of extraction time on the efficiency of an
extraction operation, obtained the data shown in the following table. Calculate r
Extraction time X
Extraction efficiency (%) y
27
57
45
64
41
80
19
46
35
62
39
72
19
52
49
77
15
57
31
68

174
Correlation coefficient Command:
This command is used to find the correlation coefficient between two variables.
R=correcoef(A,B)
Where A is a vector of variance of first variable and B is the vector of values of second variable.
This command returns the correlation coefficient between two variables A and B as a matrix.
(i)
(1,1) Elements is the correlation coefficient between A and A
(ii) (1,2) Elements is the correlation coefficient between A and B
(iii) (2,1) Elements is the correlation coefficient between B and A
(iv) (2,2) Elements is the correlation coefficient between B and B
Example:
>>
a=[ 70 92 80 74 65 83];
>>b=[
74 84 63 87 78 90];
>> r=corrcoef(a,b)
r=
1.0000
0.6474
0.6474
1.0000
Tutorial problems:
1. Show that for the Bivariate normal distribution Independence implies zero correlation.
2. The following
table gives the data on corn yield x and peanut yield (y) (mt/ha) for eight different
types of soil
X: 2.4
3.4
4.6
3.7
2.2
3.3
4.0
2.1
Y: 1.33
2.12
1.80
1.65
2.00
1.76
2.11
1.63
Find the correlation between corn yields x a peanut yield and interpret the value.

175
3. The following table gives the concentrations of two different pollutants ozone concentration x
(ppm) and secondary carbon concentration y (ug/m
3
). Find the correlation coefficient between
ozone concentration and secondary carbon concentration and interpret the values
X:
0.666
0.088
0.120
0.050
0.162
0.186
0.057
0.100
Y:
4.6
11.6
9.5
6.3
13.8
15.4
2.5
11.8
4. The following table gives the data on x=% light absorption at 5800A and y=peak photo
voltage
X:
4.0 8.7
12.7
19.1
21.4
24.6
28.9
29.8
30.5
Y: 0.12
0.28 0.55
0.68
0.85
1.02
1.15
1.34
1.29
a)
Construct a scatter plot of this data. What does it suggest?
b)
Assume that the simple linear regression model is appropriate; obtain the equation of
the estimated regression line.
c)
Predict photo voltage when % absorption is 19% and compute the value of the
corresponding residual.

176
5. Compute and interpret the correlation coefficient for the following grades of 6 students
selected at random.
Mathematics grade:
70
92
80
74
65
83
English grade:
74
84
63
87
78
90
6. The following data represent the chemistry grades for a random sample of 12 freshmen at a
certain college along with their scores on an intelligence test administered while they were still
senior in high school:

177
Student:
1
2
3
4
5
6
7
8
9
10
11
12
Test score x: 65
50
55
65
55
70
65
70
55
70
50
55
Chemistry y: 85
74
76
90
85
87
94
98
81
91
76
74
Compute and interpret the sample correlation coefficient.
7. Heavy metals can inhibit the biological treatment of waste in municipal treatment plants.
Monthly measurements were made at a state of the art treatment plant of the amount of
chromium 9ug/l) in both the influent and effluent.
Influent:
250
290
270
100
300
410
110
130
1100
Effluent:
19
10
17
11
70
60
18
30
180
a) Make a scatter plot
b) Make a scatter plot after taking the natural logarithm of both variables
c) Calculate the correlation coefficient, r, in part (a) and Part (b)
d) Comment on the appropriateness of r in each case.

178

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