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For two variables x and y, the two regression coefficients are byx = -3/2 and bxy = - 1/6. The correlation coefficient between x and y is :
- a)-1/4
- b)1/4
- c)-1/2
- d)1/2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
For two variables x and y, the two regression coefficients are byx = -...
bxy and byx both have negative sign. Therefore we have to take negative sign
bxy and byx both have negative sign. Therefore we have to take negative sign
Hence, correlation coefficient (r)
Most Upvoted Answer
For two variables x and y, the two regression coefficients are byx = -...
The correlation coefficient between two variables measures the strength and direction of the linear relationship between them. In this case, we are given the regression coefficients for both x and y, and we need to find the correlation coefficient between them.
Regression coefficients:
- The regression coefficient byx represents the slope of the regression line for predicting y from x.
- The regression coefficient bxy represents the slope of the regression line for predicting x from y.
To find the correlation coefficient, we can use the formula:
r = sqrt(byx * bxy)
where r represents the correlation coefficient.
Let's calculate the correlation coefficient using the given regression coefficients:
Given: byx = -3/2 and bxy = -1/6
Calculating the correlation coefficient:
r = sqrt((-3/2) * (-1/6))
= sqrt(1/4)
= 1/2
Therefore, the correlation coefficient between x and y is 1/2.
Explanation:
- The regression coefficients represent the relationship between x and y in terms of their slopes.
- The correlation coefficient provides a measure of the strength and direction of the linear relationship between x and y.
- In this case, since the correlation coefficient is positive (1/2), it indicates a positive linear relationship between x and y.
- A correlation coefficient of 1/2 suggests that as x increases, y tends to increase, and as x decreases, y tends to decrease, in a linear fashion.
- Option C, -1/2, is the correct answer as it matches the calculated correlation coefficient.
Regression coefficients:
- The regression coefficient byx represents the slope of the regression line for predicting y from x.
- The regression coefficient bxy represents the slope of the regression line for predicting x from y.
To find the correlation coefficient, we can use the formula:
r = sqrt(byx * bxy)
where r represents the correlation coefficient.
Let's calculate the correlation coefficient using the given regression coefficients:
Given: byx = -3/2 and bxy = -1/6
Calculating the correlation coefficient:
r = sqrt((-3/2) * (-1/6))
= sqrt(1/4)
= 1/2
Therefore, the correlation coefficient between x and y is 1/2.
Explanation:
- The regression coefficients represent the relationship between x and y in terms of their slopes.
- The correlation coefficient provides a measure of the strength and direction of the linear relationship between x and y.
- In this case, since the correlation coefficient is positive (1/2), it indicates a positive linear relationship between x and y.
- A correlation coefficient of 1/2 suggests that as x increases, y tends to increase, and as x decreases, y tends to decrease, in a linear fashion.
- Option C, -1/2, is the correct answer as it matches the calculated correlation coefficient.
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For two variables x and y, the two regression coefficients are byx = -3/2 and bxy = - 1/6. The correlation coefficient between x and y is :a)-1/4b)1/4c)-1/2d)1/2Correct answer is option 'C'. Can you explain this answer?
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