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If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?
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If for two variables X and y, the covariance ,variance of x and varian...
Calculation of Correlation Coefficient
To calculate the correlation coefficient, we need to use the formula:
Correlation coefficient (ρ) = Covariance(X, Y) / (√(Variance(X) * Variance(Y)))
Given values:
Covariance(X, Y) = 40
Variance(X) = 16
Variance(Y) = 256
Calculating the correlation coefficient:
Using the given values in the formula, we can calculate the correlation coefficient as follows:
ρ = 40 / (√(16 * 256))
Simplifying the denominator:
ρ = 40 / (√(4096))
Taking the square root of 4096:
ρ = 40 / 64
Simplifying the fraction:
ρ = 0.625
Therefore, the value of the correlation coefficient (ρ) is 0.625.
Interpreting the correlation coefficient:
The correlation coefficient ranges from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 represents no correlation.
In this case, the correlation coefficient is 0.625, which is greater than 0. This indicates a positive correlation between variables X and Y.
The positive correlation suggests that as the values of variable X increase, the values of variable Y also tend to increase.
The magnitude of the correlation coefficient (0.625) suggests that the correlation between X and Y is moderately strong.
Therefore, based on the calculated correlation coefficient, we can conclude that there is a positive and moderately strong relationship between variables X and Y.
To calculate the correlation coefficient, we need to use the formula:
Correlation coefficient (ρ) = Covariance(X, Y) / (√(Variance(X) * Variance(Y)))
Given values:
Covariance(X, Y) = 40
Variance(X) = 16
Variance(Y) = 256
Calculating the correlation coefficient:
Using the given values in the formula, we can calculate the correlation coefficient as follows:
ρ = 40 / (√(16 * 256))
Simplifying the denominator:
ρ = 40 / (√(4096))
Taking the square root of 4096:
ρ = 40 / 64
Simplifying the fraction:
ρ = 0.625
Therefore, the value of the correlation coefficient (ρ) is 0.625.
Interpreting the correlation coefficient:
The correlation coefficient ranges from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 represents no correlation.
In this case, the correlation coefficient is 0.625, which is greater than 0. This indicates a positive correlation between variables X and Y.
The positive correlation suggests that as the values of variable X increase, the values of variable Y also tend to increase.
The magnitude of the correlation coefficient (0.625) suggests that the correlation between X and Y is moderately strong.
Therefore, based on the calculated correlation coefficient, we can conclude that there is a positive and moderately strong relationship between variables X and Y.
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If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?
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If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient? 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 variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?.
If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient? 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 variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If for two variables X and y, the covariance ,variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?.
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