Bivariate data

• What do the values a and b represent in a regression line?

  • a: y-intercept, value of y when x=0
  • b: gradient, change in y for each unit increase in x
• What does the phrase "y on x" refer to?

  A regression line in the form y = a + bx
• What does PMCC stand for?

  Pearson's Product-Moment Correlation Coefficient
• What should students comment on regarding their estimates?

  • Likely reliability of the estimate
  • Factors affecting the reliability
• How does the PMCC value affect predictions?

  It indicates the reliability of predictions
• What is provided to students that does not need to be memorized?

  Formula Booklet
• How are values a and b typically found?

  Using the calculator
• What should you enter into List 1 on the calculator?

  Independent variable (x) data
• What is the first step in using the calculator for regression?

  Press CALC [F2]
• What does the regression line equation look like?

  y = a + bx
• What does List 1 contain when calculating p on q?

  q data
• What does List 2 contain when calculating p on q?

  p data
• What is the significance of the PMCC value?

  • Indicates strength of linear relationship
  • Values range from -1 to 1
• What should you do in the matching activity?

  Match tables, graphs, PMCC, equations
• What is the bonus task in practice questions?

  Calculate the PMCC for each data set
• What does the y-intercept (a) represent in a regression line?

  Value of y when x is 0
• What does the gradient (b) indicate in a regression line?

  Change in y for each unit increase in x
• Compare PMCC and Spearman’s Rank correlation coefficients.

  Similarities:

  • Values range from -1 to 1
  • Not affected by scaling data

  
  

  Differences:

  • PMCC for linear relationships
  • Spearman’s for ranked data
• What is the purpose of least squares regression lines?

  Minimize the sum of the squares of residuals
• What is a residual in regression analysis?

  Vertical difference between points and line
• Why is it important to consider outliers in regression analysis?

  They can significantly affect the regression line
• What are the aims of the regression lines lesson?

  • Calculate regression lines using formulas
  • Use calculators for regression lines
  • Understand the concept of residuals
• What is the mean point in regression analysis?

  Point where the regression line passes through
• What does it mean if the regression line predicts a decrease in sprint time?

  Training improves sprint performance
• How does the regression line relate to the training hours of a sprinter?

  More training hours predict faster sprint times
• What is the relationship between the values of a and b in regression analysis?

  • a is the y-intercept
  • b is the slope of the line
• What is the significance of calculating PMCC?

  • Assesses reliability of predictions
  • Indicates strength of correlation
• What does bivariate data involve?

  Two variables
• What is the independent variable in bivariate data?

  The variable that is manipulated
• What is the dependent variable in bivariate data?

  The variable that is measured
• What is the most appropriate way to represent bivariate data?

  A scatter diagram
• What are the types of correlation in bivariate data?

  • Weak positive correlation
  • Weak negative correlation
  • Strong positive correlation
  • Strong negative correlation
  • No correlation
• What does PMCC stand for?

  Product Moment Correlation Coefficient
• What letter is used to represent PMCC?

  The letter r
• What is the range of values for PMCC?

  Between -1 and 1
• What are the interpretations of PMCC values?

  • Strong positive linear correlation: > 0.7
  • Moderate correlation: 0.2 to 0.7
  • Weak correlation: -0.2 to 0.2
  • No linear correlation: 0
  • Strong negative linear correlation: < -0.7
  • Perfect correlation: 1 or -1
• How do you interpret an r value of 0.95?

  Very strong positive linear correlation
• What does an r value of -0.85 indicate?

  Strong negative linear correlation
• Why might the r value not tell the full story?

  It doesn't account for outliers
• What is the full name of PMCC?

  Pearson’s Product Moment Correlation Coefficient