A First Course in Quality Engineering, 2nd Edition

492 A First Course in Quality Engineering

For the numerator

x x y y x y

x y

n

i i i i

i

n

i

i

n

i

i

n

i

n

−

( )

−

(

)

= −

























=

= =

=

∑

∑ ∑

∑

1

1 1

1

For the denominator

x x y y

x

x

i

i

n

i

i

n

i

i

n

i

i

n

−

( )

















−

(

)

















=

−



= =

=

=

∑ ∑

∑

∑

1

2

1

2

2

1

1



































×

−





































=

=

∑

∑

2

2

1

2

1

n

y

y

n

i

i

i

n

i

n

Example 8.4

Calculate the correlation coefficient between dry-ability and humidity from the

data given in Table 8.3, and check if the correlation is significant.

TABLE 8.5

Calculation of the Correlation Coefcient for Example 8�4

X

1

 

(Humidity)

X

2

(Hot-air

Temperature)

X

3

(Conveyor

Speed)

Y

(Dry-

ability) X

1

Y X

1

2

Y

2

36 393 1�8 0�37 13�32 1296 0�1369

51 347 1�8 0�25 12�75 2601 0�0625

56 ...