Q. 3. For
a local departmental store, a table of Annual Expenditure
for Advertisement and corresponding sales (for that
year) is given for a number of years as below. Find
the coefficient of correlation for advertisement expenditure
(as independent variable) and sales. (June
2000)
| Advertisement
Expenditure in Thousand Rupees |
0.45 |
0.55 |
0.72 |
0.83 |
1.25 |
| Sales
in Thousand Rupees |
70 |
81 |
83 |
85 |
91 |
Solution.
Let advertisement expenditure (thousand rupees) =
x
Let sales (thousand rupees) = y
| x |
y |
x2
|
y2
|
x X y |
|
0.45 |
70 |
0.2025
|
4900
|
31.5
|
|
0.55 |
81 |
0.3025
|
6561
|
44.55
|
|
0.72 |
83 |
0.5184
|
6889
|
59.76
|
|
0.83 |
85 |
0.6889
|
7225
|
70.55
|
|
1.25 |
91 |
1.5625
|
8281
|
113.75
|
|
å x = 3.80
|
å y = 410
|
å
x2 = 3.2748 |
å
y2 = 33856 |
å
xy = 320.11 |
Here, n = 5
| |
|
[n å
xy - (å x X
å y)]
|
| r = |
|
|
| |
|
{[n å
x2 - (å
x)2] X [n å
y2 - (å
y)2]}
|
| |
|
[(5 X 320.11) - (3.80 X 410)]
|
| or r = |
|
|
| |
|
{[(5 X 3.278) - (3.80)2]
X [(5 X 33856) - (410)2]}
|
or r = 0.89
|
