[DATA] American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.
a. Which variable is the explanatory variable based on the goals of the research?


b. Draw a scatter diagram of the data.

Verified step by step guidance

1. Step 1: Identify the variables involved in the study. Here, the two variables are the length of the bear and the weight of the bear.
2. Step 2: Determine the explanatory (independent) variable and the response (dependent) variable based on the research goal. Since the goal is to predict the bear's weight from its length, the length is the explanatory variable, and the weight is the response variable.
3. Step 3: To draw a scatter diagram, label the horizontal axis (x-axis) with the explanatory variable, which is the bear's length.
4. Step 4: Label the vertical axis (y-axis) with the response variable, which is the bear's weight.
5. Step 5: Plot each pair of data points (length, weight) on the graph by placing a point where the length value on the x-axis corresponds to the weight value on the y-axis.

Key Concepts

Explanatory and Response Variables

In statistical modeling, the explanatory variable (independent variable) is the one used to predict or explain changes in another variable, called the response variable (dependent variable). Here, since the goal is to predict bear weight, length is the explanatory variable, and weight is the response variable.

Scatter Diagram

A scatter diagram is a graphical representation that plots paired data points on a coordinate plane, showing the relationship between two quantitative variables. It helps visualize patterns, trends, or correlations, such as how bear length might relate to weight.

Correlation and Relationship Between Variables

Correlation measures the strength and direction of a linear relationship between two variables. Understanding this helps determine if length is a good predictor of weight, which is essential before building a predictive model.