Chapter 7, Problem 11E

(a)

To determine

To identify which of the correlation given in the question belongs to the scatterplot given in the subparts.

Answer to Problem 11E

  $0.006$ .

Explanation of Solution

The given list of correlations are: $-0.923,-0.487,0.006\text{ and 0}\text{.777}$ .

Thus, by looking at the scatterplot of part (a), we can say that it does not have a linear association and also its correlation coefficient should be very close to zero since the points in this scatterplot is spread in downward curve. Thus, the correlation that best fits to it is $0.006$ .

(b)

To determine

To identify which of the correlation given in the question belongs to the scatterplot given in the subparts.

Answer to Problem 11E

  $0.777$ .

Explanation of Solution

The given list of correlations are: $-0.923,-0.487,0.006\text{ and 0}\text{.777}$ .

Thus, by looking at the scatterplot of part (b), we can say that it is the only with a positive linear association and its correlation coefficient should be close to one as the points in the scatterplot shows that they are going in an upward direction so the relationship is positive and none other graph has positive association. Thus, the correlation that best fits to it is $0.777$ .

(c)

To determine

To identify which of the correlation given in the question belongs to the scatterplot given in the subparts.

Answer to Problem 11E

  $-0.923$ .

Explanation of Solution

The given list of correlations are: $-0.923,-0.487,0.006\text{ and 0}\text{.777}$ .

Thus, by looking at the scatterplot of part (c), we can say that it has a linear negative association as the points in the scatterplot is going downward but the points in the scatterplot in part (d) is also going downward, since the points in scatterplot of part (c) shows much more clustered in shape as in part (d) thus part (c) scatterplot should have a correlation coefficient much closer to $-1$ than that of part (d). Thus, the correlation that best fits to it is $-0.923$ .

(d)

To determine

To identify which of the correlation given in the question belongs to the scatterplot given in the subparts.

Answer to Problem 11E

  $-0.487$ .

Explanation of Solution

The given list of correlations are: $-0.923,-0.487,0.006\text{ and 0}\text{.777}$ .

Thus, by looking at the scatterplot of part (d), we can say that it isit has a linear negative association as the points in the scatterplot is going downward but the points in the scatterplot in part (c) is also going downward, since the points in scatterplot of part (c) shows much more clustered in shape as in part (d) thus part (d) scatterplot should have a correlation coefficient less closer to $-1$ than that of part (c). Thus, the correlation that best fits to it is $-0.487$ .