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Chapter 2: Q5 (page 74)

Scatterplot. In Exercises 5鈥�8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation?

Brain Volume and IQ The table lists brain volumes (cm3 ) and IQ scores of five males (from Data Set 8 鈥淚Q and Brain Size鈥� in Appendix B).

Brain Volume

1173

1067

1347

1029

1204

IQ

101

93

94

97

113

Short Answer

Expert verified

The scatterplot is constructed as shown below:

By observing the scatterplot, it can be seen that the points do not lie close to a straight-line pattern. Thus, the two variables, IQ score and brain volume, are not linearly correlated.

Step by step solution

01

Given information

The observations of two variables, namely IQ score and brain volume (in ), are known.

Brain volume

1173

1067

1347

1029

1204

IQ

101

93

94

97

113

02

Construct the scatterplot

A scatterplot is graphed for a paired set of values with each of the variables scaled on the horizontal and vertical axes.

Use the following steps to plot a scatterplot between IQ score and brain volume:

  • Consider x as brain volume and y as IQ score.
  • Mark the values 90, 100, and so on until 120 on the vertical axis.
  • Mark the values 1000, 1100, 1200, and so on until 1400 on the horizontal axis.
  • Plot the points on the graph corresponding to the pair of values for the two variables.
  • Label the horizontal axis as 鈥淏rain Volume鈥� and the vertical axis as 鈥淚Q score.鈥�

The following scatterplot is generated:

03

Analyzing the scatterplot

Linear correlation is implied by the visual inspection of a scatterplot; if the points on the plot tend to follow a linear pattern.

It can be observed that the points do not lie close to a straight-line pattern and are randomly scattered.

Therefore, it can be concluded that IQ score and brain volume are not linearly related.

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