Question

the errors in predicting hurricane tracks are given in nautical miles. a statutory mile is 0.86898 nautical mile. most people living on the gulf coast of the united states would prefer to know the prediction errors in statutory miles rather than nautical miles. explain why converting the errors to miles would not change the correlation between prediction error and year. choose the correct answer below. a. the correlation will not change because it treats x and y symmetrically. the correlation of x with y is the same as the correlation of y with x. b. the correlation will not change because it is based on the sample size. c. the correlation will not change because it is based on the standard deviations of the two variables. the standard deviation of the prediction error is the same regardless of the units. d. the correlation will not change because it is based on standardized values (z - scores). the z - scores of the prediction errors are the same regardless of the units.

Explanation:

Step1: Recall correlation property

Correlation coefficient \(r\) is based on standardized values (z - scores) of variables \(x\) and \(y\). It treats \(x\) and \(y\) symmetrically and is unit - less.

Step2: Analyze each option

Option A correctly states that the correlation will not change because it treats \(x\) and \(y\) symmetrically. The correlation of \(y\) with \(x\) is the same as the correlation of \(x\) with \(y\). Option B is wrong as correlation is not based on sample size. Option C is wrong as it is not based on standard deviation in the sense described. Option D is wrong as correlation is based on standardized values not just regardless of units in a non - standardized way.

Answer:

A. The correlation will not change because it treats x and y symmetrically. The correlation of y with x is the same as the correlation of x with y.