Advertisements
Advertisements
Question
Calculate the coefficient of correlation for the ages of husbands and their respective wives:
| Age of husbands | 23 | 27 | 28 | 29 | 30 | 31 | 33 | 35 | 36 | 39 |
| Age of wives | 18 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 32 |
Solution
Without deviation:
| Age of husbands (X) | Age of wives (Y) | X2 | Y2 | XY |
| 23 | 18 | 529 | 324 | 414 |
| 27 | 22 | 729 | 484 | 594 |
| 28 | 23 | 784 | 529 | 644 |
| 29 | 24 | 841 | 576 | 696 |
| 30 | 25 | 900 | 625 | 750 |
| 31 | 26 | 961 | 676 | 806 |
| 33 | 28 | 1089 | 784 | 924 |
| 35 | 29 | 1225 | 841 | 1015 |
| 36 | 30 | 1296 | 900 | 1080 |
| 39 | 32 | 1521 | 1024 | 1248 |
| 311 | 257 | 9875 | 6763 | 8171 |
∑X = 311, ∑Y = 257, ∑X2 = 9875, ∑Y2 = 6763, ∑XY = 8171
N = 10
Coefficient of correlation
r = `("N"sum"XY" - (sum"X")(sum"Y"))/(sqrt("N"sum"X"^2 - (sum"X")^2) sqrt ("N"sum"Y"^2 - (sum"Y")^2))`
= `(10 xx 8171 - 311 xx 257)/(sqrt (10 xx 9875 - (311)^2) sqrt(10 xx 6763 - (257)^2))`
= `(81710 - 79927)/(sqrt (98750 - 96721) sqrt (67630 - 66049))`
= `1783/(45 xx 39.76)`
= 0.9965
APPEARS IN
RELATED QUESTIONS
In the following data one of the value of y is missing. Arithmetic means of x and y series are 6 and 8 respectively. `(sqrt(2) = 1.4142)`
| x | 6 | 2 | 10 | 4 | 8 |
| y | 9 | 11 | ? | 8 | 7 |
Estimate missing observation.
Calculate the correlation coefficient for the following data.
| X | 5 | 10 | 5 | 11 | 12 | 4 | 3 | 2 | 7 | 1 |
| Y | 1 | 6 | 2 | 8 | 5 | 1 | 4 | 6 | 5 | 2 |
Find the coefficient of correlation for the following:
| Cost (₹) | 14 | 19 | 24 | 21 | 26 | 22 | 15 | 20 | 19 |
| Sales (₹) | 31 | 36 | 48 | 37 | 50 | 45 | 33 | 41 | 39 |
Calculate the coefficient of correlation between X and Y series from the following data.
| Description | X | Y |
| Number of pairs of observation | 15 | 15 |
| Arithmetic mean | 25 | 18 |
| Standard deviation | 3.01 | 3.03 |
| Sum of squares of deviation from the arithmetic mean | 136 | 138 |
Summation of product deviations of X and Y series from their respective arithmetic means is 122.
Example for positive correlation is
If the values of two variables move in same direction then the correlation is said to be
From the following data, N = 11, ∑X = 117, ∑Y = 260, ∑X2 = 1313, ∑Y2 = 6580, ∑XY = 2827 the correlation coefficient is
The correlation coefficient is
The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is
If Cov(x, y) = – 16.5, `sigma_"x"^2` = 2.89, `sigma_"y"^2` = 100. Find correlation coefficient.
