Chapter 3.1, Problem 28E

(a)

To determine

Scatterplot for the relationship between price and profit.

Explanation of Solution

Given information:

Prices of the bench and corresponding average profits:

  

For scatterplot:

Horizontal axis: Price

Vertical axis: Average profit

  

(b)

To determine

Whether the correlation of these data can be true although having a strong relationship between price and average profit.

Answer to Problem 28E

The correlation measures only strength of relationship between the variables, while the variables possess quadratic relationship.

Explanation of Solution

Given information:

Prices of the bench and corresponding average profits:

  

At $r=0$ ,

The correlation measures only the strength of linear relationship between the variables.

That implies

No linear relationship exists between price and average profit.

However,

That does not mean that variables do not have any relationship between them.

Note that

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