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Chapter 4: Problem 24

The correlation between house price (in dollars) and area of the house (in square feet) for some houses is 0.91. If you found the correlation between house price in thousands of dollars and area in square feet for the same houses, what would the correlation be?

Short Answer

Expert verified
The correlation remains the same, which is 0.91, even if the units of the variables change.

Step by step solution

01

Understanding Correlation Coefficient

A correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables. Importantly for this exercise, correlation coefficients are unitless and invariant under change of scale. Therefore, if we change the units of the variables, the correlation does not change.
02

Applying to our Problem

Since we are dealing with the same dataset, and the correlation coefficient is unitless and invariant under change of scale, changing the units (i.e., from dollars to thousands of dollars) doesn't affect the correlation. Thus the correlation remains the same.
03

The Solution

The correlation between house price (now in thousands of dollars) and the area of the house (in square feet) remains at 0.91.

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Most popular questions from this chapter

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