Question

A carpenter sells handmade wooden benches at a craft fair every week. Over the past year, the carpenter has varied the price of the benches from $\backslash (80$

to $\backslash )120$ and recorded the average weekly profit he made at each selling price. The prices of the bench and the corresponding average profits are shown in the table.

a. Make a scatterplot to show the relationship between price and profit.

b. The correlation for these data is $r=0$Explain how this can be true even though there is a strong relationship between price and average profit.

Short answer

Part (b) The correlation measures only the strength of the relationship between the variables, while the variables possess a quadratic relationship.

Part (a)

Step-by-step solution

Part (a) Step 1: Given information

Prices of the bench and corresponding average profits:

Part (a) Step 2: Explanation

For scatterplot:

Horizontal axis: Price

Vertical axis: Average profit

Part (b) Step 1: Explanation

At $r=0$

Only the strength of the linear link between the variables is measured by the correlation.

That implies

No linear relationship exists between price and average profit.

However,

That does not rule out the possibility of a link between variables.

Note that

Since all the points lie on the same parabola that opens downward, variables possess a perfect quadratic relationship between them.