Q. 3.1 The scatterplots below show four... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 3: Q. 3.1 (page 154)

The scatterplots below show four sets of real data:
(a) repeats the manatee plot in Figures
(b) shows the number of named tropical storms and the number predicted before the start of hurricane season each year between $1984$ and $2007$ by William Gray of Colorado State University;
(c) plots the healing rate in micrometers (millionths of a meter) per hour for the two front limbs of several newts in an experiment; and
(d) shows stock market performance in consecutive years over a $56$ -year period.
For each graph, estimate the correlation r. Then interpret the value of r in context.
(a)
(b)
(c)
(d)

Short Answer

Expert verified

The values of r are:

(a) $r = 0.90$

(b) $r = 0.50$

(d) $r = - 0.40$

Step by step solution

Given Information

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

Scatterplot (a): indicates the manatee plot.

Scatterplot (b): indicates the number of named tropical storms.

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

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

Explanation

The correlation determines whether the variables on the $y -$ axis and $x -$ axis have a positive or negative connection. Thus, looking at the scatterplot (a), we can observe that the points are oriented upwards from left to right, indicating that the association is positive, and that the points are closer to a line, indicating that the correlation is close to one. As a result, $r = 0.90$ could be found in scatterplot (a). This indicates a significant and positive relationship between the variables. The points in scatterplot (b) are oriented upwards from left to right, indicating that the relationship is positive, but the points are not particularly close to a line. As a result, $r = 0.50$ could be found in scatterplot (b).

This indicates a weak but favorable relationship between the variables. We can observe from the scatterplot (c) that the dots are distributed far apart, thus they don't form any pattern and aren't close to any line. As a result, could be found in scatterplot (c).

This indicates that the variables have no relationship. Looking at the scatterplot (d), we can see that the points are moving downwards from left to right, indicating that the association is negative. However, the points are not getting any closer to a line and are becoming more dispersed. As a result, $r = - 0.40$ could be found in scatterplot (d). This means that the association between the variables is weak and negative.