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If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?
- a)0.4
- b)0.5
- c)0.6
- d)0.7
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the covariance between x and y is 30, variance of x is 25 and varia...
cov(x,y) = 30
var(x) = 25; var(j) = 144
Most Upvoted Answer
If the covariance between x and y is 30, variance of x is 25 and varia...
Calculation:
Given:
Covariance (x, y) = 30
Variance (x) = 25
Variance (y) = 144
To find:
Correlation coefficient (ρ)
Steps:
Step 1: Calculate the standard deviation of x (σx) and y (σy) using the variance.
Standard deviation (σ) = √(variance)
σx = √(25) = 5
σy = √(144) = 12
Step 2: Calculate the correlation coefficient (ρ) using the formula:
ρ = Covariance (x, y) / (σx * σy)
ρ = 30 / (5 * 12)
ρ = 30 / 60
ρ = 0.5
Therefore, the correlation coefficient between x and y is 0.5.
Explanation:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
In this case, the covariance between x and y is 30, which indicates a positive linear relationship. However, the covariance value alone does not provide a clear measure of the strength of the relationship. Therefore, we need to calculate the correlation coefficient.
By calculating the standard deviation of x and y, we can determine the spread or variability of the data. The standard deviation of x is 5, indicating that the values of x are relatively close to the mean. Similarly, the standard deviation of y is 12, indicating a wider spread of y values.
Using the formula for correlation coefficient, we divide the covariance by the product of the standard deviations. The resulting correlation coefficient is 0.5, which indicates a moderate positive linear relationship between x and y.
Conclusion:
The correlation coefficient between x and y is 0.5, indicating a moderate positive linear relationship between the variables.
Given:
Covariance (x, y) = 30
Variance (x) = 25
Variance (y) = 144
To find:
Correlation coefficient (ρ)
Steps:
Step 1: Calculate the standard deviation of x (σx) and y (σy) using the variance.
Standard deviation (σ) = √(variance)
σx = √(25) = 5
σy = √(144) = 12
Step 2: Calculate the correlation coefficient (ρ) using the formula:
ρ = Covariance (x, y) / (σx * σy)
ρ = 30 / (5 * 12)
ρ = 30 / 60
ρ = 0.5
Therefore, the correlation coefficient between x and y is 0.5.
Explanation:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
In this case, the covariance between x and y is 30, which indicates a positive linear relationship. However, the covariance value alone does not provide a clear measure of the strength of the relationship. Therefore, we need to calculate the correlation coefficient.
By calculating the standard deviation of x and y, we can determine the spread or variability of the data. The standard deviation of x is 5, indicating that the values of x are relatively close to the mean. Similarly, the standard deviation of y is 12, indicating a wider spread of y values.
Using the formula for correlation coefficient, we divide the covariance by the product of the standard deviations. The resulting correlation coefficient is 0.5, which indicates a moderate positive linear relationship between x and y.
Conclusion:
The correlation coefficient between x and y is 0.5, indicating a moderate positive linear relationship between the variables.
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If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?a)0.4b)0.5c)0.6d)0.7Correct answer is option 'B'. Can you explain this answer?
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