Regression coefficients are independent of change of scale and origin.

Answer

To determine whether the statement "Regression coefficients are independent of change of scale and origin" is true or false, we will analyze the components involved in calculating the regression coefficients.

### Step-by-Step Solution:

1. **Understanding Regression Coefficients**:
The regression coefficient \( b_{xy} \) (the slope of the regression line of Y on X) is given by the formula:
\[ b_{xy} = r_{xy} \frac{\sigma_y}{\sigma_x} \]
where:
- \( r_{xy} \) is the correlation coefficient between X and Y.
- \( \sigma_x \) is the standard deviation of X.
- \( \sigma_y \) is the standard deviation of Y.

2. **Analyzing the Correlation Coefficient**:
The correlation coefficient \( r_{xy} \) is a measure of the strength and direction of the linear relationship between two variables. It is independent of the scale and origin, meaning that if we change the units of measurement for X or Y (scale) or shift the values (origin), the correlation coefficient remains the same.

3. **Standard Deviations and Their Dependence**:
The standard deviations \( \sigma_x \) and \( \sigma_y \) are affected by changes in scale and origin. If we transform the variable X to a new variable U using the formula \( U = aX + b \), the new standard deviation \( \sigma_u \) will be affected by the scaling factor \( a \). Specifically:
\[ \sigma_u = |a| \sigma_x \]
This indicates that standard deviations are dependent on the scale and origin.

4. **Combining the Results**:
Since \( b_{xy} \) depends on both the correlation coefficient \( r_{xy} \) (which is independent of scale and origin) and the standard deviations \( \sigma_x \) and \( \sigma_y \) (which are dependent on scale and origin), the overall regression coefficient \( b_{xy} \) is influenced by changes in scale and origin.

5. **Conclusion**:
Therefore, the statement "Regression coefficients are independent of change of scale and origin" is **false**.

### Final Answer:
The statement is **false**.