Linear correlation 573
X
Y
x = (X − X )
y = (Y − Y )
13
11
3.75
−7.25
X = 111, X =
111
12
= 9.25
Y = 219, Y =
219
12
= 18.25
x y
x 2
y 2
45.3
52.6
39.1
39.3
18.1
85.6
32.8
39.1
27.6
7.6
7.6
7.6
−5.9
22.6
1.6
−8.4
5.1
14.1
−79.7
39.1
162.6
539.1
351.6
826.6
−5.9
22.6
1.6
18.6
5.1
68.1
57.8
39.1
85.6
−27.2
14.1
52.6
x y = 613.4
x 2 = 616.7
y 2 = 1372.7
The coefficient of correlation,
r =
x y
x 2
y 2
=
613.4
√
{(616.7)(1372.7)}
= 0.667
Thus, there is no appreciable correlation between
petrol and car sales.
Now try the following exercise
Exercise 217 Further problems on linear
correlation
In Problems 1 to 3, determine the coefficient of
correlation for the data given, correct to 3 decimal
places.
1. X
14
18
23
30
50
Y 900 1200 1600 2100 3800
[0.999]
2. X
2.7 4.3
1.2
1.4 4.9
Y 11.9 7.10 33.8 25.0 7.50
[−0.916]
3. X 24 41
9 18 73
Y 39 46 90 30 98
[0.422]
4. In an experiment to determine the relationship
between the current flowing in an electrical
circuit and the applied voltage, the results
obtained are:
Current
(mA)
5 11 15 19 24 28 33
Applied
voltage (V) 2 4 6 8 10 12 14
Determine, using the product-moment formula, the coefficient of correlation for these
results.
[0.999]
5. A gas is being compressed in a closed cylinder
and the values of pressures and corresponding
volumes at constant temperature are as shown:
Pressure (kPa) Volume (m 3 )
160
0.034
180
0.036
200
0.030
220
0.027
240
0.024
260
0.025
280
0.020
300
0.019
Find the coefficient of correlation for these
values.
[−0.962]
6. The relationship between the number of miles
travelled by a group of engineering salesmen
in ten equal time periods and the corresponding value of orders taken is given below.
Calculate the coefficient of correlation using
the product-moment formula for these values.
X
Y
x = (X − X )
y = (Y − Y )
13
11
3.75
−7.25
X = 111, X =
111
12
= 9.25
Y = 219, Y =
219
12
= 18.25
x y
x 2
y 2
45.3
52.6
39.1
39.3
18.1
85.6
32.8
39.1
27.6
7.6
7.6
7.6
−5.9
22.6
1.6
−8.4
5.1
14.1
−79.7
39.1
162.6
539.1
351.6
826.6
−5.9
22.6
1.6
18.6
5.1
68.1
57.8
39.1
85.6
−27.2
14.1
52.6
x y = 613.4
x 2 = 616.7
y 2 = 1372.7
The coefficient of correlation,
r =
x y
x 2
y 2
=
613.4
√
{(616.7)(1372.7)}
= 0.667
Thus, there is no appreciable correlation between
petrol and car sales.
Now try the following exercise
Exercise 217 Further problems on linear
correlation
In Problems 1 to 3, determine the coefficient of
correlation for the data given, correct to 3 decimal
places.
1. X
14
18
23
30
50
Y 900 1200 1600 2100 3800
[0.999]
2. X
2.7 4.3
1.2
1.4 4.9
Y 11.9 7.10 33.8 25.0 7.50
[−0.916]
3. X 24 41
9 18 73
Y 39 46 90 30 98
[0.422]
4. In an experiment to determine the relationship
between the current flowing in an electrical
circuit and the applied voltage, the results
obtained are:
Current
(mA)
5 11 15 19 24 28 33
Applied
voltage (V) 2 4 6 8 10 12 14
Determine, using the product-moment formula, the coefficient of correlation for these
results.
[0.999]
5. A gas is being compressed in a closed cylinder
and the values of pressures and corresponding
volumes at constant temperature are as shown:
Pressure (kPa) Volume (m 3 )
160
0.034
180
0.036
200
0.030
220
0.027
240
0.024
260
0.025
280
0.020
300
0.019
Find the coefficient of correlation for these
values.
[−0.962]
6. The relationship between the number of miles
travelled by a group of engineering salesmen
in ten equal time periods and the corresponding value of orders taken is given below.
Calculate the coefficient of correlation using
the product-moment formula for these values.