[DATA] Bear Markets A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) for a sample of bear markets.
a. Treating the length of the bear market as the explanatory variable, draw a scatter diagram of the data.

Verified step by step guidance

1. Step 1: Identify the variables for the scatter diagram. The explanatory variable (independent variable) is the length of the bear market in months, and the response variable (dependent variable) is the percent change in the S&P 500 index.
2. Step 2: Label the horizontal axis (x-axis) as 'Months' and the vertical axis (y-axis) as 'Percent Change'. This setup reflects that the percent change depends on the length of the bear market.
3. Step 3: Plot each pair of data points from the table on the graph. For each row, find the value of 'Months' on the x-axis and the corresponding 'Percent Change' on the y-axis, then mark a point at that coordinate.
4. Step 4: After plotting all points, observe the overall pattern or trend in the scatter diagram. This can help in understanding the relationship between the length of the bear market and the percent change.
5. Step 5: Optionally, add a title to the scatter diagram such as 'Scatter Diagram of Bear Market Length vs. Percent Change' to clearly indicate what the graph represents.

Key Concepts

Scatter Diagram

A scatter diagram is a graphical representation that displays the relationship between two quantitative variables. Each point on the plot corresponds to one observation with coordinates representing the values of the two variables. It helps visualize patterns, trends, or correlations between variables, such as the length of bear markets and their percent changes.

Explanatory and Response Variables

In statistical analysis, the explanatory variable (independent variable) is the one that is presumed to influence or predict changes in another variable, called the response variable (dependent variable). Here, the length of the bear market (months) is the explanatory variable, and the percent change in the S&P 500 is the response variable.

Correlation and Association

Correlation measures the strength and direction of a linear relationship between two variables. Understanding whether longer bear markets are associated with larger percent declines involves assessing correlation. A scatter plot helps identify if a positive, negative, or no correlation exists between months and percent change.