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Magazine Chapter 2: Q6 (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?
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 鈥淏ear Measurements鈥� 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 鈥淐hest (in)鈥� and the vertical axis as 鈥淲eight (lb).鈥�
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.
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