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?

Bear Measurements The table lists chest sizes (distance around chest in inches) and weights (pounds) of anesthetized bears that were measured (from Data Set 9 “Bear Measurements” in Appendix B).

Chest (in.)	26	45	54	49	35
Weight (lb)	80	344	416	348	166

Short answer

The scatterplot is constructed as shown below:

By observing the scatterplot, it can be seen that the points lie close to a straight-line pattern. Thus, the two variables, weight and chest size, are linearly correlated.

Step-by-step solution

Given information

Two variables, namely chest sizes (in.) and weights (lb) of anaesthetized bears are recorded.

Chest sizes(in)	26	45	54	49	35
Weights (lb)	80	344	416	348	166

Construct the scatterplot

A scatterplot graphs values of two quantitative variables pair-wise such that one variable is marked on the horizontal axis and the other on the vertical axis.

Use the following steps to plot a scatter plot between weight and chest size:

• Consider x as the chest size and y as weight.
• Mark the values 20, 25, and so on until 60 on the horizontal axis.
• Mark the values 50, 100, and so on till 1400 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 “Chest (in)” and the vertical axis as “Weight (lb).”

The following scatterplot is generated:

Analyzing the scatterplot

When the observed points corresponding to the observations fall in a straight-line pattern on a scatterplot, the variables can be inferred as linearly correlated.

It can be observed that the points lie close to a straight-line pattern such that with an increase in chest size, the weight increases steadily.

Therefore, it can be concluded that the weight and chest sizes of anaesthetized bears are linearly correlated in a positive direction.