Chapter 3.1, Problem 3.1CYU

To determine

To estimate the correlation r for each graph and then interpret the value of r in context.

Answer to Problem 3.1CYU

Scatterplot (a) may have $r=0.90$ , scatterplot (b) may have $r=0.50$ , scatterplot (c) may have $r=0$ and scatterplot (d) may have $r=-0.40$ .

Explanation of Solution

The scatterplot is shown in the question for the four set of real data namely as,

Scatterplot (a): shows the manatee plot.

Scatterplot (b): shows number of named tropical storms.

Scatterplot (c): shows the plot healing rate in micrometers.

Scatterplot (d): shows the stock market performance in consecutive years.

The correlation interprets the positive and negative relationship between the variables on y -axis and x -axis. Thus, by looking at the scatterplot (a), we can see that the points is from the left to right direction upwards so this means that the association is positive and the points are closer to a line so the correlation may be close to one. So, scatterplot (a) may have $r=0.90$ . This means that the association between the variables is strong and positive.

By looking at the scatterplot (b), we can see that the points are from the left to right direction upwards so this means that the association is positive but the points are not much closer to a line. So, scatterplot (b) may have $r=0.50$ . This means that the association between the variables is weak and positive. By looking at the scatterplot (c), we can see that the points are scattered far from each other so they does not form any pattern and are not close to any line. So, scatterplot (c) may have $r=0$ . This means that there is no association between the variables. By looking at the scatterplot (d), we can see that the points are from the left to right direction downwards so this means that the association is negative but the points are not much closer to a line and they are scattered more. So, scatterplot (d) may have $r=-0.40$ . This means that the association between the variables is weak and negative.