Correlation

• Bivariate data


  Data which has pairs of values for two variables
• Scatter diagram


  • Represents bivariate data
• Independent or explanatory variable


  Something which the researcher can control, usually plotted on the x-axis
• Dependent or response variable


  Measured by the researcher, usually plotted on the y-axis
• Correlation


  Describes the nature of linear relationships between two variables
• Negative correlation


  One variable decreases when the other increases
• Positive correlation


  One variable increases with the increase of the other variable
• Causal relationship


  A change in one variable causes a change in the other
• Example 1: Study of a city

  • Distance from city centre (km)
  • Population density (people/hectare)
• As distance from the centre increases


  The population density decreases
• Regression line


  Line of best fit which minimises the sum of the squares of the distances of each datapoint from the line
• Regression line equation


  y = a + bx
• Coefficient b


  Tells you the change in y for each unit change in x
• For positively correlated data, b is positive
• For negatively correlated data, b is negative
• Interpolation


  Substituting a known value of the independent variable into x to estimate the corresponding value of the dependent variable, within the range of data given
• Extrapolation


  Estimating a value of x for a given value of y, outside the range of data given, which is much less reliable
• Example 2: Daily mean windspeed and daily maximum gust


  • Regression line equation: g = 7.23 + 1.82w
• The daily maximum gust is expected to increase by approximately 1.8 knots when the daily mean windspeed increases by 1 knot
• Predicted daily maximum gust when daily mean speed is 16 knots is 36.35 knots