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?

Heights of Fathers and Sons The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton).

Height of father	Height of first son (in.)
73	74
75.5	73.5
75	71
75	70.5
75	72
74	76.5
74	74
73	71
73	72
78.5	73.2

Short answer

The scatterplot is constructed as shown below:

Observing the scatterplot shows that the points do not lie close to a straight-line pattern and are randomly scattered. Thus, the two variables, the height of the father and height of the first son, are not linearly correlated.

Step-by-step solution

Given information

Observations are recorded for two variables: the height of the father (in inches) and the height of the first son (in inches).

Height of father	Height of first son (in.)
73	74
75.5	73.5
75	71
75	70.5
75	72
74	76.5
74	74
73	71
73	72
78.5	73.2

Construct the scatterplot

A scatterplot describes the linear correlation between two variables if the points are arranged in a linear trend.

Use the following steps to plot a scatter plot between the height of the father and the height of the first son:

• Consider x as the height of the father (in.) and y as the height of the first son (in.).
• Mark the values 72, 73, and so on until 79 on the horizontal axis.
• Mark the values 70, 71, and so on until 77 on the vertical axis.
• Plot the points on the graph corresponding to the pairs of values for the two variables.
• Label the horizontal axis as “Height of father (in.)” and the vertical axis as “Height of the first son (in.).”

The following scatterplot is generated:

Analyze the scatterplot

When the scatterplot is observed, the points seem to be scattered far from each other such that there is no linear pattern between the observations.

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

Therefore, it can be concluded that the height of the father and the height of the first son are not linearly related.