Final answer:
The true or false statement regards the coefficient of correlation 'r', which remains unaffected by scaling or shifting data, making the answer True.
Step-by-step explanation:
The statement "The value of r does not change with scaling or shifting." is seeking a True or False answer, where the context suggests that 'r' refers to the coefficient of correlation. This coefficient measures the strength and direction of the linear relationship between two variables, and indeed, it is not affected by either scaling (multiplying all values by a constant) or shifting (adding a constant to all values). Therefore, the answer is True.
When data is scaled, although the individual values for each point on the axes change, the overall shape of the data and the relationships between the points remain the same. Hence, the correlation coefficient stays constant.
Similarly, when data is shifted (meaning adding or subtracting a constant from all data points), the relative distances between the points don't change; it's just that the entire set of points moves up or down on the graph together. This does not affect the straightness or slope of the line of best fit, and therefore the correlation coefficient, 'r', remains unchanged.