Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).
a. Treating the length of the bull 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 plot. The explanatory variable (independent variable) is the length of the bull market in months ("Bull Months"), and the response variable (dependent variable) is the percentage change in the S&P 500 ("Percent Change").
2. Step 2: Set up the coordinate system for the scatter plot. Label the horizontal axis (x-axis) as "Bull Months" and the vertical axis (y-axis) as "Percent Change".
3. Step 3: For each bull market data point, plot a point on the graph where the x-coordinate corresponds to the "Bull Months" value and the y-coordinate corresponds to the "Percent Change" value. For example, the first data point is (4.9, 46.77), so place a point at x=4.9 and y=46.77.
4. Step 4: Repeat the plotting for all 25 data points from the table, ensuring each point accurately represents the pair of values from the two columns.
5. Step 5: After plotting all points, review the scatter diagram to observe any patterns or relationships between the length of the bull market and the percent change in the S&P 500.

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 values of the explanatory and response variables. It helps visualize patterns, trends, or correlations between variables, such as the length of bull markets and their percent changes.

Explanatory and Response Variables

In statistical analysis, the explanatory variable (independent variable) is the factor that is manipulated or categorized to observe its effect on another variable, called the response variable (dependent variable). Here, the length of the bull 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 quantitative variables. A positive correlation means that as one variable increases, the other tends to increase as well. Understanding correlation helps interpret the scatter diagram and assess whether longer bull markets are associated with higher percent changes.