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The correlation coefficient between two variables X and Y is 0.4. The correlation coefficient between 2X and (-Y) will be:
- a)0.4
- b)-0.8
- c)-0.4
- d)0.8
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The correlation coefficient between two variables X and Y is 0.4. The ...
Correlation Coefficient
The correlation coefficient is a statistical measure that quantifies 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, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.
Given Information
- Correlation coefficient between variables X and Y = 0.4
Determining the Correlation Coefficient between 2X and (-Y)
To determine the correlation coefficient between 2X and (-Y), we need to understand how changes in X and Y affect the new variables.
Relationship between 2X and X
Multiplying a variable by a constant does not change the direction of the linear relationship. However, it does affect the strength of the relationship. In this case, multiplying X by 2 will double the values of X but preserve the direction of the relationship.
Relationship between (-Y) and Y
Negating a variable changes the direction of the linear relationship. In this case, multiplying Y by -1 will reverse the direction of the relationship.
Calculating the Correlation Coefficient
To calculate the correlation coefficient between 2X and (-Y), we need to multiply the correlation coefficient between X and Y by the correlation coefficient between 2X and (-Y).
Given:
- Correlation coefficient between X and Y = 0.4
Multiplying X by 2 (2X) doubles the values of X, but the direction of the relationship remains the same. Therefore, the correlation coefficient between X and 2X will remain the same as the correlation coefficient between X and Y, which is 0.4.
Multiplying Y by -1 (-Y) reverses the direction of the relationship. Therefore, the correlation coefficient between Y and (-Y) will be -1.
Now, we can multiply the correlation coefficient between X and 2X (0.4) by the correlation coefficient between Y and (-Y) (-1) to find the correlation coefficient between 2X and (-Y).
0.4 * (-1) = -0.4
Therefore, the correlation coefficient between 2X and (-Y) is -0.4, which corresponds to option C.
The correlation coefficient is a statistical measure that quantifies 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, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.
Given Information
- Correlation coefficient between variables X and Y = 0.4
Determining the Correlation Coefficient between 2X and (-Y)
To determine the correlation coefficient between 2X and (-Y), we need to understand how changes in X and Y affect the new variables.
Relationship between 2X and X
Multiplying a variable by a constant does not change the direction of the linear relationship. However, it does affect the strength of the relationship. In this case, multiplying X by 2 will double the values of X but preserve the direction of the relationship.
Relationship between (-Y) and Y
Negating a variable changes the direction of the linear relationship. In this case, multiplying Y by -1 will reverse the direction of the relationship.
Calculating the Correlation Coefficient
To calculate the correlation coefficient between 2X and (-Y), we need to multiply the correlation coefficient between X and Y by the correlation coefficient between 2X and (-Y).
Given:
- Correlation coefficient between X and Y = 0.4
Multiplying X by 2 (2X) doubles the values of X, but the direction of the relationship remains the same. Therefore, the correlation coefficient between X and 2X will remain the same as the correlation coefficient between X and Y, which is 0.4.
Multiplying Y by -1 (-Y) reverses the direction of the relationship. Therefore, the correlation coefficient between Y and (-Y) will be -1.
Now, we can multiply the correlation coefficient between X and 2X (0.4) by the correlation coefficient between Y and (-Y) (-1) to find the correlation coefficient between 2X and (-Y).
0.4 * (-1) = -0.4
Therefore, the correlation coefficient between 2X and (-Y) is -0.4, which corresponds to option C.
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Community Answer
The correlation coefficient between two variables X and Y is 0.4. The ...
Given
The correlation coefficient between two variables X and Y = 0.4
Concept used
The correlation coefficient (r) is independent of origin and scale and depend on the sign of variables
Calculation
The correlation coefficient between the two variables is the measure of the slope between the variables in the regression graph. It is given that the correlation coefficient between X and Y is 0.4 and the correlation coefficient is independent of change of origin and scale but it depends on variables
∴ The correlation coefficient between 2X and (-Y) is - 0.4
Important Points:
The value of simple correlation coefficient in the interval of [-1, 1]
The regression coefficient is independent of the change of origin. But, they are not independent of the change of the scale. It means there will be no effect on the regression coefficient if any constant is subtracted from the values of x and y
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