Chapter 9: Correlations

Introduction to Correlations

• Correlations are connections between two types of quantitative measurements.
• Example: Sales (in thousands of dollars) and Advertising dollars spent (also in thousands).
• Objective: Determine if there is a connection between these variables.

Scatter Plots

• Definition: A graph that represents data points with dots.
• Each dot represents two numerical measures for a single entity (e.g., a month).
• Axes Representation:
  • X-axis (horizontal): e.g., Sales.
  • Y-axis (vertical): e.g., Advertising dollars.
  • Each axis has a number scale relevant to the data.

Understanding Correlations

• Types of Correlations:
  • Positive Correlation: Dots seem to follow an upward trend.
  • Negative Correlation: Dots seem to follow a downward trend.
  • No Correlation: Dots do not follow any discernible pattern.
  • Nonlinear (Curvilinear) Correlation: Dots follow a curve rather than a straight line.
• Descriptors: Correlations can be described as strong, moderate, or weak based on how closely the dots follow a regression line.
• Regression Line: An invisible line that the dots seem to align with, also called the line of best fit.
• The steepness of the line does not indicate strength; proximity of dots to the line does.

Correlation Coefficient (R)

• R Value: A statistical measure that indicates the strength and direction of a correlation.
• R ranges from -1 to +1.
  • -1: Perfect negative correlation.
  • 0: No correlation.
  • +1: Perfect positive correlation.

R Value Scale (for class purposes)

• No Correlation: R value between -0.25 and +0.25.
• Weak Correlation: R value between -0.50 to -0.25 or +0.25 to +0.50.
• Moderate/Regular Correlation: R value between -0.75 to -0.50 or +0.50 to +0.75 (no descriptor needed).
• Strong Correlation: R value between -1.00 to -0.75 or +0.75 to +1.00.

Calculating the Correlation Coefficient

• Use technology (e.g., calculators) to compute the R value.
• Procedure:
  1. Enter data into lists (e.g., L1 for chirps, L2 for temperature).
  2. Use the linear regression function (LinReg) to calculate R.
  3. Ensure diagnostics are on to display R and R² values.
• Interpretation Example:
  • Calculated R value = 0.958 indicates a strong positive correlation.

Skills Acquired

• Calculate the correlation coefficient (R).
• Describe the type and strength of correlation based on R value.