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14.28 Sloppy writing about correlation. Each of the following statements contains a blunder. Explain in each...

14.28 Sloppy writing about correlation. Each of the following statements contains a blunder. Explain in each case what is wrong. (a) “There is a high correlation between the manufacturer of a car and the gas mileage of the car.” (b) “We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car.” (c) “The correlation between the weight of a car and the gas mileage of the car was found to be r = 0.53 miles per gallon.”

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Answer #1

(A) it is given that there is a high correlation between the ,manufacturer of a car and the gas mileage of the car. We know that the correlation coefficient is calculated only for two numerical data set and the car manufacturer is not numerical data set. therefore, given statement is incorrect

(B) we know that the maximum correlation value is 1 and minimum is -1. So, we can never a correlation coefficient of 1.09, this means that the given statement is incorrec

(C) we know that the correlation coefficient is a constant value which is calculated using the ratio of standard deviations, which means that it will have no unit. So, given correlation of r = 0.53 miles per gallon is incorrect because correlation can never be expressed in units.

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