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If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps
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If for two variable x and y the covariance, variance of x and variance...
Given: cov(x y)=40 var(x)=16 var(y)=256SD(x)=4 SD(y)=16cov(x y)÷SD(x).SD(y)40÷4.16=0.625
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If for two variable x and y the covariance, variance of x and variance...
Calculating Correlation Coefficient
To calculate the correlation coefficient, we need to use the formula:
r = cov(x,y) / (σx * σy)
where r is the correlation coefficient, cov(x,y) is the covariance between x and y, σx is the standard deviation of x, and σy is the standard deviation of y.
Given Information:
- Covariance (cov) = 40
- Variance (σ^2) of x = 16
- Variance (σ^2) of y = 256
Calculating Standard Deviations:
We need to calculate the standard deviations of x and y before we can calculate the correlation coefficient.
σx = sqrt(σ^2 of x) = sqrt(16) = 4
σy = sqrt(σ^2 of y) = sqrt(256) = 16
Calculating Correlation Coefficient:
Now we can substitute the values we have into the formula for the correlation coefficient:
r = cov(x,y) / (σx * σy)
r = 40 / (4 * 16)
r = 0.625
Therefore, the correlation coefficient between x and y is 0.625.
Conclusion:
The correlation coefficient ranges from -1 to 1. A value of 0 means there is no correlation between the variables, a positive value means there is a positive correlation, and a negative value means there is a negative correlation. In this case, a correlation coefficient of 0.625 indicates a moderately strong positive correlation between x and y.
To calculate the correlation coefficient, we need to use the formula:
r = cov(x,y) / (σx * σy)
where r is the correlation coefficient, cov(x,y) is the covariance between x and y, σx is the standard deviation of x, and σy is the standard deviation of y.
Given Information:
- Covariance (cov) = 40
- Variance (σ^2) of x = 16
- Variance (σ^2) of y = 256
Calculating Standard Deviations:
We need to calculate the standard deviations of x and y before we can calculate the correlation coefficient.
σx = sqrt(σ^2 of x) = sqrt(16) = 4
σy = sqrt(σ^2 of y) = sqrt(256) = 16
Calculating Correlation Coefficient:
Now we can substitute the values we have into the formula for the correlation coefficient:
r = cov(x,y) / (σx * σy)
r = 40 / (4 * 16)
r = 0.625
Therefore, the correlation coefficient between x and y is 0.625.
Conclusion:
The correlation coefficient ranges from -1 to 1. A value of 0 means there is no correlation between the variables, a positive value means there is a positive correlation, and a negative value means there is a negative correlation. In this case, a correlation coefficient of 0.625 indicates a moderately strong positive correlation between x and y.
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If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps
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If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps .
If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If for two variable x and y the covariance, variance of x and variance of your are 40, 16 and 256 respectively, what is the value of the correlation coefficient?pls do show the steps .
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