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Chapter 5: Problem 12

An auction house released a list of 25 recently sold paintings. Eight artists were represented in these sales. The sale price of each painting also appears on the list. Would the correlation coefficient be an appropriate way to summarize the relationship between artist \((x)\) and sale price \((y)\) ? Why or why not?

Short Answer

Expert verified
No, the correlation coefficient would not be an appropriate method to summarize the relationship between the artist (which is a categorical variable) and the sale price (which is a numerical variable).

Step by step solution

01

Understanding the correlation coefficient

The correlation coefficient, also known as Pearson correlation coefficient, is a measure of the strength and direction of linear relationship between two variables, in this case, between artist and sale price. It does not capture non-linear relationships or multiple categories effectively.
02

Interpreting the given context

In this context, the artist variable is categorical, not numerical, with eight discrete categories each representing one artist. The sale price is numerical. The correlation coefficient is best suited to explain the relationship between two numerical variables, not between a numerical and a categorical variable.
03

Answer to the question

Thus, the correlation coefficient would not be an appropriate method to summarize the relationship between the artist and the sale price. It does not take into account the categories of artists and cannot fully describe the possible variations in sale price between different artists.

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Most popular questions from this chapter

Explain why it can be dangerous to use the leastsquares line to obtain predictions for \(x\) values that are substantially larger or smaller than those contained in the sample.

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