Higher Engineering Mathematics, Sixth Edition

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.

1. X^1418233050
   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 for-

mula, 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 correspond-
   ing value of orders taken is given below.
   Calculate the coefficient of correlation using
   the product-moment formula for these values.