Advertisements
Advertisements
Question
Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.
Solution
Given, n = 50, `sigma_"x"` = 4.8, `sigma_"y"` = 3.5, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 420
Cov (x, y) = `1/"n" sum("x"_"i" - bar"x")("y"_"i" - bar"y")`
= `1/50 xx 420`
∴ Cov (x, y) = 8.4
r = `("Cov" ("x", "y"))/(sigma_"x" sigma_"y")`
= `(8.4)/((4.8)(3.5)`
= `(84 xx 10)/(48 xx 35)`
= `1/2`
= 0.5
APPEARS IN
RELATED QUESTIONS
Find correlation coefficient between x and y series for the following data.
n = 15, `bar"x"` = 25, `bar"y"` = 18, σx = 3.01, σy = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122
The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.
Find correlation coefficient from the following data. `["Given:" sqrt(3) = 1.732]`
| x | 3 | 6 | 2 | 9 | 5 |
| y | 4 | 5 | 8 | 6 | 7 |
Find the number of pairs of observations from the following data,
r = 0.15, `sigma_"y"` = 4, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 12, `sum("x"_"i" - bar"x")^2` = 40.
Given that r = 0.4, `sigma_"y"` = 3, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 108, `sum("x"_"i" - bar"x")^2` = 900. Find the number of pairs of observations.
Given the following information, `sum"x"_"i"^2` = 90, `sum"x"_"i""y"_"i"` = 60, r = 0.8, `sigma_"y"` = 2.5, where xi and yi are the deviations from their respective means, find the number of items.
A sample of 5 items is taken from the production of a firm. Length and weight of 5 items are given below. [Given : `sqrt(0.8823)` = 0.9393]
| Length (cm) | 3 | 4 | 6 | 7 | 10 |
| Weight (gm.) | 9 | 11 | 14 | 15 | 16 |
Calculate the correlation coefficient between length and weight and interpret the result.
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between 2x and y
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between `"x"/2` and y
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x and 3y
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x – 5 and y – 3
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x + 7 and y + 9
In the calculation of the correlation coefficient between the height and weight of a group of students of a college, one investigator took the measurements in inches and pounds while the other investigator took the measurements in cm. and kg. Will they get the same value of the correlation coefficient or different values? Justify your answer.
