BIVARIATE DATA(2)

• Correlation analysis


  The degree of relationship between the variables under consideration
• Correlation coefficient


  The measure of correlation
• Purpose of correlation analysis

  • To discover whether there is a relationship between variables
  • To find out the direction of the relationship whether it is positive, negative or zero
  • To find the strength of the relationship between the two variables
• Types of correlation


  • Kendall Rank Correlation
  • Spearman Rank Correlation
  • Pearson r Correlation
  • Pearson Product Correlation Coefficient
• Kendall Rank Correlation


  A non-parametric test that measures the strength of dependence between two variables
• Spearman Rank Correlation


  A non-parametric test used to measure the degree of association between two variables
• Pearson r Correlation


  Widely used in statistics to measure the degree of relationship between linear related variables
• Pearson Product Correlation Coefficient

  Denoted by r, measures the strength of the linear relationship
• Interpretation of Pearson Product Correlation Coefficient (r)

  • +1: Perfect positive correlation
  • +0.71 to +0.99: Strong positive correlation
  • +0.51 to +0.70: Moderately positive correlation
  • +0.31 to +0.50: Weak positive correlation
  • +0.01 to +0.30: Negligible positive correlation
  • 0: No correlation
  • -0.01 to -0.30: Negligible negative correlation
  • -0.31 to -0.5: Weak negative correlation
  • -0.51 to -0.70: Moderately negative correlation
  • -0.71 to -0.99: Strong negative correlation
  • -1: Perfect negative correlation
• Example 1


  • Time spent studying (x) and test scores (y) of 6 grade 11 students
• Solving for Pearson Product Correlation Coefficient

  1. Create a table

  2. Substitute to the formula

  3. Interpret the result
• Seatwork 3


  • Number of selfies (x) posted on Facebook and science test scores (y)
• Regression analysis


  A technique of studying the dependence of one variable (dependent variable) on one or more variables (explanatory variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables
• Regression equation


  The equation of the regression line
• Example 1


  • Data on x and y variables
  • Find the equation of the regression line
  • Draw the graph of the regression equation on the scatter plot
  • Estimate the value of y if x=9
• Example 2


  • Data on x and y variables
  • Find the equation of the regression line
  • Draw the graph of the regression equation on the scatter plot
  • Estimate the value of y if x=8