Lecture Notes: Scatter Diagrams in Operations Management

Introduction to Scatter Diagrams

• Definition: Scatter diagrams, also known as scatter plots or scatter charts, are graphs used to plot two variables against each other to identify potential relationships or correlations.
• Purpose: To determine if there is a relationship between two variables by plotting them as coordinates on a graph and observing trends or correlations.

Examples of Scatter Diagrams

Example 1: Car Weight vs. Gas Mileage

• X-axis: Car weight
• Y-axis: Gas mileage
• Observation: As car weight increases, gas mileage decreases (negative correlation).

Example 2: Vehicle Speed vs. Stopping Distance

• X-axis: Vehicle speed
• Y-axis: Stopping distance
• Observation: As speed increases, stopping distance also increases (positive correlation).

Analyzing Scatter Diagrams

• Trend Lines: Linear lines added to scatter plots to illustrate the relationship between variables.
  • Downward trend line: Indicates a negative correlation (one variable increases as the other decreases).
  • Upward trend line: Indicates a positive correlation (both variables increase together).
  • No Correlation: The variables do not show any clear trend.

Creating a Scatter Plot in Excel

1. Data Input: Enter data into two columns (X and Y coordinates).
2. Plot Creation:
   • Select XY or scatter plot from chart tools.
3. Chart Customization:
   • Add axis titles.
   • Add a trend line (typically starts as a linear trend line).
   • Include R² (coefficient of determination) for further analysis.

Understanding Statistical Measures

• Coefficient of Determination (R²):

  • Falls between 0 and 1.
  • Higher values indicate a better explanation of the relationship between variables.

• Correlation Coefficient (R):

  • Known as the square root of the coefficient of determination.
  • Values:
    • Greater than 0.8: Strong relationship
    • Less than 0.5: Weak relationship

Conclusion

• Purpose of Scatter Plots: To examine and understand the relationship between two variables.
• Transition to future topics on the seven tools of quality in upcoming sessions.