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
xy 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
∑
xy= 613. 4
∑
x^2 = 616. 7
∑
y^2 = 1372. 7
The coefficient of correlation,
r=
∑
xy
√{(∑
x^2
)(∑
y^2
)}
=
613. 4
√
{( 616. 7 )( 1372. 7 )}
= 0. 667
Thus, there isno appreciable correlationbetween
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.
- X^1418233050
Y 900 1200 1600 2100 3800
[0.999] - X 2.7 4.3 1.2 1.4 4.9
Y 11.9 7.10 33.8 25.0 7.50
[−0.916] - X 24 41 9 18 73
Y 39 46 90 30 98
[0.422] - 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 for-
mula, the coefficient of correlation for these
results. [0.999]
- 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]
- The relationship between the number of miles
travelled by a group of engineering salesmen
in ten equal time periods and the correspond-
ing value of orders taken is given below.
Calculate the coefficient of correlation using
the product-moment formula for these values.