Page 164 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
60—70 65 + 3 9 300 + 115 13,225 + 345
70—80 75 + 4 16 500 + 315 99,225 + 1,260
N = 8 ∑d x ∑d x 2 ∑ d y ∑d y 2 ∑dd y
x
= 4 = 44 = +3 = 1,57,425 = 2,311

( )∑ ( d d ) ∑
∑dd y – x y
x
r = N ( 2
∑ x – ( 2 x )∑d 2 ∑d d y 2 – y ) ∑d
N N

N = 8, ∑dd y = 2,311, ∑d = 4, ∑ d = 3, ∑d x 2 = 44,
x
y
x
2
∑d y = 1,57,425
Substituting these values
()( ) 3
2311 – 4 2309.5
r = =
() 4 2 () 3 2 42 157423.88
44 – 157425 –
8 8
2309.5 2309.5
= = = 0.898.
6.4807 × 396.77 2571.34
Correlation of Grouped Data

When the number of observations of X and Y variables is large, the data are often classified into two-
way frequency distribution called a correlation table. The class intervals for Y are listed in the captions
or column headings, and those for X are listed in the stubs at the left of the table (the order can also be
reversed). The frequencies for each cell of the table are determined by either tallying or sorting just as
in the case of a frequency distribution of a single variable.
The formula for calculating the coefficient of correlation is:

( )∑ ( fd fd ) ∑
∑ fd d y – x y
x
r = N 2
( )∑ fd 2 ( y ) ∑ fd
∑ x 2 – x ∑ fd fd y 2 –
N N

Note: The formula is the same as the one discussed above for assumed mean. The only difference
is that here the deviations are also multiplied by the frequencies.
Steps

(i) Take the step deviations of variable X and denote these deviations by d .
x
(ii) Take the step deviations of the variable Y and denote these deviations by d .
y
(iii) Multiply d d and the respective frequency of each cell and write the figure obtained in the
x y
right hand upper corner of each cell.
(iv) Add together all the cornered values as calculated in step (iii) and obtain the total ∑ f d .
x y
(v) Multiply the frequencies of the variable X by the deviations of X and obtain the total ∑ fd .
x

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