Data was gathered from several homes for sale in Columbus, Ohio, to examine the relationship between the size of the house (measured in square feet) and the price of the house (measured in dollars). Suppose you learn the relationship between size and price is linear, positive, and strong. A correlation coefficient, $ r $, is computed, and a regression equation is constructed to predict house price based on house size.

What would the units of $ r $ be equal to in this case?

1. Dollars per square foot
2. Square feet per dollar
3. Dollars
4. Square feet
5. $ r $ has no units

The correlation coefficient (r) does not have any units. It is a unitless measure and is not expressed in terms of dollars, square feet, or any other specific unit.

Therefore, the correct answer is 5. r has no units.

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JohnRogerStephens JohnRogerStephens · Answer 2 · 2023-12-13T00:39:02-05:00

Final answer:

The correlation coefficient r, representing the strength and direction of the linear relationship between house size and price, is a unitless measure and hence wouldn't have any units in this context.

Explanation:

In the context of the correlation between the size and price of homes in Columbus, Ohio, the units of the correlation coefficient, referred to as r, would not have any units. The correlation coefficient r is a dimensionless measure that ranges between -1 and +1 and represents the strength and direction of the linear association between two variables. Therefore, when dealing with house size in square feet and house price in dollars, r does not take on the units of these variables but instead remains unitless. It simply quantifies the strength and direction of the linear relationship.

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