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If a constant 60 is subtracted from each of the values of X and Y, then the regression coefficient is
- a)reduced by 60
- b)increased by 60
- c)1/60th of the original regression coefficient
- d)not changed
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If a constant 60 is subtracted from each of the values of X and Y, the...
The regression coefficient are independent of the change of the 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
∴ After subtracting constant 60 from each value of X and Y, the regression coefficient is not changed.
Most Upvoted Answer
If a constant 60 is subtracted from each of the values of X and Y, the...
Understanding Regression Coefficients
When performing linear regression, the regression coefficient measures the relationship between the independent variable (X) and the dependent variable (Y). It indicates how much Y is expected to change with a one-unit change in X.
Effect of Subtracting a Constant
When a constant value is subtracted from both X and Y, the following occurs:
- The regression equation generally takes the form: Y = a + bX.
- If we subtract a constant (60 in this case) from both X and Y, the new equation becomes: (Y - 60) = a + b(X - 60).
Analyzing the New Equation
- The slope (b) of the regression line remains the same because it reflects the rate of change between X and Y.
- The subtraction of the constant does not affect the relationship between the two variables, hence the slope (regression coefficient) does not change.
Conclusion
Thus, when a constant is subtracted from both X and Y:
- The regression coefficient remains unchanged.
- Therefore, the correct answer to the question is option 'D': not changed.
This principle is critical in statistics, ensuring that the relationship quantified by regression analysis remains valid regardless of constant shifts in the data.
When performing linear regression, the regression coefficient measures the relationship between the independent variable (X) and the dependent variable (Y). It indicates how much Y is expected to change with a one-unit change in X.
Effect of Subtracting a Constant
When a constant value is subtracted from both X and Y, the following occurs:
- The regression equation generally takes the form: Y = a + bX.
- If we subtract a constant (60 in this case) from both X and Y, the new equation becomes: (Y - 60) = a + b(X - 60).
Analyzing the New Equation
- The slope (b) of the regression line remains the same because it reflects the rate of change between X and Y.
- The subtraction of the constant does not affect the relationship between the two variables, hence the slope (regression coefficient) does not change.
Conclusion
Thus, when a constant is subtracted from both X and Y:
- The regression coefficient remains unchanged.
- Therefore, the correct answer to the question is option 'D': not changed.
This principle is critical in statistics, ensuring that the relationship quantified by regression analysis remains valid regardless of constant shifts in the data.
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