True-False questions. Assume that all of the assumptions for correlation and lin

Question

True-False questions. Assume that all of the assumptions for correlation and linear regression have been met (including the assumption that the X and Y variables are each normally distributed). In your write-up, just list the sub-question letter (A-J) and whether the statement is True or False – no need to restate the question or to justify your answer.

A. Correlation always implies causation.
B. If a correlation is negative, then as it becomes even more negative, r2 increases.
C. If the units used to measure the Y variable change (like from inches to centimeters), then the value of r will change.  
D. As |r| increases, the average deviation of data from the predicted value (according to the best-fit regression line) increases.
E. The best-fit regression line to predict Y when you know X will always go through the point ZX = 0 and ZY = 0.
F. If a positive correlation exists between X and Y, and the range of X is then greatly restricted, |r| must increase.
G. If a positive correlation exists between X and Y, and a new data point is added whose ZX = 3 and ZY = 0, the correlation will decrease. (Note: for G, H, I, and J, assume there are many, many data points in the dataset, so that the introduction of new data points doesn’t change the values of the averages in any meaningful way.)
H. If no correlation exists between X and Y, and a new data point is added whose ZX = 2.5 and ZY = 2.5, r will decrease.
I. If a positive but imperfect correlation exists between X and Y, and a new data point is added whose ZX = 2.5 and ZY = 2.5, |r| will increase.
J. If a negative correlation exists between X and Y, and a new data point is added whose ZX = 2.5 and ZY = 2.5, |r| will decrease.

Explanation / Answer

A. Correlation always implies causation.   

[FALSE. Correlation does not imply causation.]

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B. If a correlation is negative, then as it becomes even more negative, r2 increases.

[TRUE. for negative values, the more it decreases, the more it is close to -1, which has greater r^2.]

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C. If the units used to measure the Y variable change (like from inches to centimeters), then the value of r will change.

[FALSE. COnversion does not change r.]

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D. As |r| increases, the average deviation of data from the predicted value (according to the best-fit regression line) increases.

[FALSE. It decreases. It becomes a better fit.]

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