Chapter 4, Problem 4.57RE

(a)

To determine

To construct the scatterplot for the following data given in the question.

Explanation of Solution

The scatterplot for the data is:

  

(b)

To determine

To show that the correlation is about $0.5$ using the method of example $4.5$ .

Explanation of Solution

  

  $\begin{array}{l}\overline{x}=5\\ \text{Standard deviation of }x=4\\ \overline{y}=4\\ \text{Standard deviation of }y=3.742\end{array}$

Calculating standardized value of $y\text{ and }x$ and then multiplying corresponding standardized value and then adding them together and finally dividing them by $n-1=5$ .

(c)

To determine

To find out the feature of the data that is responsible for reducing the correlation to this value despite a strong straight line association between $y\text{ and }x$ in most of the observation.

Explanation of Solution

The fifth data point disrupts the strong correlation because of this the data that is responsible for reducing the correlation to this value despite a strong straight line association between $y\text{ and }x$ in most of the observation.