chapter 4

• What is the purpose of scatter diagrams?

  To show relationships between two variables
• What is plotted on the x-axis of a scatter diagram?

  Explanatory variable (independent variable)
• What is plotted on the y-axis of a scatter diagram?

  Response variable (dependent variable)
• How should points be plotted on a scatter diagram?

  With crosses, not joined up
• What does correlation refer to?

  The relationship between two variables
• What is positive correlation?

  As one variable increases, so does the other
• What is negative correlation?

  As one variable increases, the other decreases
• What indicates zero correlation?

  The points are randomly scattered
• What is linear correlation?

  Points lie close to a straight line
• What is causation?

  One variable causes a change in another
• Does correlation imply causation?

  No, correlation does not imply causation
• What do multiple factors in real-life situations indicate?

  Multiple factors interact to cause changes
• What does a positive correlation between fat in liver and reaction time suggest?

  It does not imply one causes the other
• What is the Line of Best Fit (LOBF)?

  • A straight line through scatter points
  • Points are evenly scattered on either side
  • Must be close to as many points as possible
  • Goes through the mean point
• What does a closer point to the LOBF indicate?

  The stronger the correlation
• What is the mean point in a scatter diagram?

  (Mean of x values, Mean of y values)
• What is interpolation?

  Making predictions within the range of data
• What is extrapolation?

  Making predictions outside the range of data
• Why is extrapolation less reliable?

  Trends may change outside the range
• What is the equation of the LOBF?

  $y =$$ax +$$b$
• What does 'a' represent in the LOBF equation?

  The gradient of the line
• What does 'b' represent in the LOBF equation?

  The y-intercept of the line
• How do you find the gradient 'a'?

  $a =$$\frac{y_2 - y_1}{x_2 - x_1}$
• How can you find the y-intercept 'b'?

  Use $b =$$y_1 - ax_1$
• What does Spearman’s Rank Correlation Coefficient (SRCC) measure?

  The strength of correlation between two variables
• What is the range of SRCC values?

  Between -1 and 1
• What does a value of rs near 1 indicate?

  Strong positive correlation
• What does a value of rs near -1 indicate?

  Strong negative correlation
• What does a value of rs equal to 0 indicate?

  Zero correlation
• What does Pearson’s Product Moment Correlation Coefficient (PMCC) measure?

  The strength of linear correlation
• What is the range of PMCC values?

  Between -1 and 1
• What does a value of r near 1 indicate?

  Strong positive correlation
• What does a value of r near -1 indicate?

  Strong negative correlation

  
• Compare SRCC and PMCC.

  • SRCC: Measures correlation strength between two variables
  • PMCC: Measures strength of linear correlation
  • SRCC: Can test for linear and non-linear correlation
  • PMCC: Tests only for linear correlation
  • SRCC: Best for ranked data
  • PMCC: Can be used for non-ranked data
• What happens if there is a non-linear positive relationship?

  SRCC will be closer to 1 than PMCC
• What happens if there is a non-linear negative relationship?

  SRCC will be closer to -1 than PMCC