Question

Scatterplot. In Exercises 5–8, 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 “IQ and Brain Size” in Appendix B).

Brain Volume	1173	1067	1347	1029	1204
IQ	101	93	94	97	113

Short answer

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

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

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 “Brain Volume” and the vertical axis as “IQ score.”

The following scatterplot is generated:

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.