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(Direction 3 - 26) Answer the following questions by writing the correct answers. Each question carries 2 marks.
Q. If for two variable 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?
- a)0.01
- b)0.625
- c)0.4
- d)0.5
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
(Direction 3 - 26)Answer the following questions by writing the correc...
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It is denoted by the symbol 'r'.
Given:
Covariance (cov) = 40
Variance (var) of x = 16
Variance (var) of y = 256
We can use the formula for the correlation coefficient to find its value.
Calculation:
1. Calculate the standard deviation of x and y:
Standard deviation (SD) of x = √var(x) = √16 = 4
Standard deviation (SD) of y = √var(y) = √256 = 16
2. Calculate the correlation coefficient (r):
r = cov / (SD of x * SD of y)
r = 40 / (4 * 16)
r = 40 / 64
r = 0.625
Therefore, the value of the correlation coefficient is 0.625.
Explanation of the steps:
1. Standard deviation (SD) is calculated by taking the square root of the variance. In this case, the variance of x is given as 16, so the standard deviation of x is √16 = 4. Similarly, the variance of y is given as 256, so the standard deviation of y is √256 = 16.
2. The correlation coefficient is calculated using the formula r = cov / (SD of x * SD of y). The covariance is given as 40. Plugging in the values, we get r = 40 / (4 * 16) = 0.625.
Interpretation:
The correlation coefficient ranges from -1 to +1. A positive value indicates a positive linear relationship between the variables, while a negative value indicates a negative linear relationship. The closer the value is to 1 or -1, the stronger the relationship. In this case, the correlation coefficient is 0.625, which indicates a moderately strong positive linear relationship between the variables x and y.
Summary:
The value of the correlation coefficient for the given variables x and y is 0.625, indicating a moderately strong positive linear relationship between them.
Given:
Covariance (cov) = 40
Variance (var) of x = 16
Variance (var) of y = 256
We can use the formula for the correlation coefficient to find its value.
Calculation:
1. Calculate the standard deviation of x and y:
Standard deviation (SD) of x = √var(x) = √16 = 4
Standard deviation (SD) of y = √var(y) = √256 = 16
2. Calculate the correlation coefficient (r):
r = cov / (SD of x * SD of y)
r = 40 / (4 * 16)
r = 40 / 64
r = 0.625
Therefore, the value of the correlation coefficient is 0.625.
Explanation of the steps:
1. Standard deviation (SD) is calculated by taking the square root of the variance. In this case, the variance of x is given as 16, so the standard deviation of x is √16 = 4. Similarly, the variance of y is given as 256, so the standard deviation of y is √256 = 16.
2. The correlation coefficient is calculated using the formula r = cov / (SD of x * SD of y). The covariance is given as 40. Plugging in the values, we get r = 40 / (4 * 16) = 0.625.
Interpretation:
The correlation coefficient ranges from -1 to +1. A positive value indicates a positive linear relationship between the variables, while a negative value indicates a negative linear relationship. The closer the value is to 1 or -1, the stronger the relationship. In this case, the correlation coefficient is 0.625, which indicates a moderately strong positive linear relationship between the variables x and y.
Summary:
The value of the correlation coefficient for the given variables x and y is 0.625, indicating a moderately strong positive linear relationship between them.
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Community Answer
(Direction 3 - 26)Answer the following questions by writing the correc...
R = (cov x,y )
_____
sx² . sy²
= 256
____
40². 16²
= 256
____
1600 . 256
= 256
_____
409600
= 0.000625
_____
sx² . sy²
= 256
____
40². 16²
= 256
____
1600 . 256
= 256
_____
409600
= 0.000625
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(Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer?
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(Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer? 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 (Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer?.
(Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer? 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 (Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (Direction 3 - 26)Answer the following questions by writing the correct answers. Each question carries 2 marks.Q.If for two variable 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?a)0.01b)0.625c)0.4d)0.5Correct answer is option 'B'. Can you explain this answer?.
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