Chapter 9, Problem 14E

To determine

To match each point given in the scatterplot from (a-e) with the correct new correlation from the list given in the question.

Answer to Problem 14E

  Point (a) has $r=0.85$ .

  Point (b) has $r=0.05$ .

  Point (c) has $r=0$ .

  Point (d) has $r=-0.45$ .

  Point (e) has $r=-0.30$ .

Explanation of Solution

The scatterplot shows five blue data points whose correlation is $r=0$ . And also the scatterplot has five green points at different positions from the previous position. And it produces a regression line with slope zero. We have to find out the correct correlation from the list that matches the point. Thus the list of the correlations given in the question is:

  $-0.45,-0.30,0,0.05,0.85$

Thus, now we look at the positions of the points. By looking at the point (a) we can see that the point is positive and in the upward direction from the rest of the points therefore it will be related to positive correlation thus, point (a) has $r=0.85$ . By looking at point (b) we can see that the point is below the point (a) and more towards the zero therefore, point (b) has $r=0.05$ . By looking at the point (c) we can say that it is far more near to the zero from the other points and therefore, point (c) will have $r=0$ . Now, by looking at the point (d) we can see that it is below the points (a), (b) and (c) but above the point (e) and it is also downward sloping therefore, point (d) will have $r=-0.45$ . And at last the point (e) which is very below the other points and is negative as it shows downward slope therefore, the point (e) will have $r=-0.30$ .