Chapter 3.1, Problem 15E

(a)

To determine

To match:the given graph to the $\gamma$ below

Answer to Problem 15E

The best Correlation is $\gamma =0.9$

Explanation of Solution

Given:

  

  $\begin{array}{l}\gamma =-0.9\\ \gamma =-0.7\\ \gamma =-0.3\\ \gamma =0\\ \gamma =0.3\\ \gamma =0.7\\ \gamma =0.9\end{array}$

Calculation:

The overall pattern in figure moves from lower left to upper right. We call this a positive association between the two variables. The form of the relationship is linear. That is, the overall pattern follows a straight line from lower left to upper right. The relationship is strong because the points don’t deviate greatly from line. When scatterplot is comparedto the given figures, then

Correlation $\gamma =0.9$ is the best one.

(b)

To determine

To match: the given graph to the $\gamma$ below

Answer to Problem 15E

The best Correlation is $\gamma =0$

Explanation of Solution

Given:

  

  $\begin{array}{l}\gamma =-0.9\\ \gamma =-0.7\\ \gamma =-0.3\\ \gamma =0\\ \gamma =0.3\\ \gamma =0.7\\ \gamma =0.9\end{array}$

Calculation:

The overall pattern in figure (b) is not in line. The form of the relationship is not linear. The relationship is very weak because the points don’t show any relation. When scatterplot is comparedto the given figures, then

Correlation $\gamma =0$ is the best one.

(c)

To determine

To match: the given graph to the $\gamma$ below

Answer to Problem 15E

The best Correlation is $\gamma =0.7$

Explanation of Solution

Given:

  

  $\begin{array}{l}\gamma =-0.9\\ \gamma =-0.7\\ \gamma =-0.3\\ \gamma =0\\ \gamma =0.3\\ \gamma =0.7\\ \gamma =0.9\end{array}$

Calculation:

The overall pattern in figure(c) moves from lower left to upper right. We call this a positive association between the two variables. The form of the relationship is linear. That is, the overall pattern follows a straight line from lower left to upper right. The relationship is not very strong because the points deviate greatly from line. When scatterplot is comparedto the given figures, then

Correlation $\gamma =0.7$

(d)

To determine

To match: the given graph to the $\gamma$ below

Answer to Problem 15E

The best Correlation is $\gamma =-0.3$

Explanation of Solution

Given:

  

  $\begin{array}{l}\gamma =-0.9\\ \gamma =-0.7\\ \gamma =-0.3\\ \gamma =0\\ \gamma =0.3\\ \gamma =0.7\\ \gamma =0.9\end{array}$

Calculation:

The overall pattern in figure (d) moves from upper left to lower right. We call this a negative association between the two variables. The form of the relationship is linear. That is, the overall pattern follows a straight line from upper left to lower right. The relationship is very weak because the points deviate greatly from line. When scatterplot is comparedto the given figures, then

Correlation $\gamma =-0.3$

(e)

To determine

To match: the given graph to the $\gamma$ below

Answer to Problem 15E

The best Correlation is $\gamma =-0.9$

Explanation of Solution

Given:

  

  $\begin{array}{l}\gamma =-0.9\\ \gamma =-0.7\\ \gamma =-0.3\\ \gamma =0\\ \gamma =0.3\\ \gamma =0.7\\ \gamma =0.9\end{array}$

Calculation:

The overall pattern in figure moves from upper left to lower right. We call this a negative association between the two variables. The form of the relationship is linear. That is, the overall pattern follows a straight line from upper left to lower right. The relationship is very strong because the points don’t deviate greatly from line. When scatterplot is comparedto the given figures, then

Correlation $\gamma =-0.9$