The correct answer is: A. The signs of the regression coefficients are always the same.
The other options are all true statements.
- B. Correlation coefficient is the geometric mean of the two regression coefficients.
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated by dividing the covariance between the two variables by the product of their standard deviations. The correlation coefficient can range from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
- C. The covariance between two variables divided by the product of their standard deviations produces the value of coefficient of correlation.
This is the formula for calculating the correlation coefficient.
- D. Coefficient of correlation is independent of origin but not of scale.
This means that the correlation coefficient is not affected by the units of measurement of the variables, but it is affected by the location of the origin. For example, the correlation coefficient between height and weight would be the same for people measured in inches and pounds as it would be for people measured in centimeters and kilograms. However, the correlation coefficient would be different if the origin were changed, such as if the height of everyone were increased by 6 inches.