Simple Linear Regression (DP IB Business Management)

Interpreting Scatter Graphs

• Scatter graphs allow businesses to compare two variables such as sales volume and advertising to establish if there is any correlation between them

Diagram: typical scatter graph

Types of correlation

• A correlation exists where there is a relationship or connection between two variables 

• A positive correlation means as one variable increases, so does the other variable

  • A line of best fit that slopes upwards can be identified 

• A negative correlation means as one variable increases, the other variable decreases

  • A line of best fit that slopes downwards can be identified 

• No correlation means there is no connection between the two variables

  • It is not possible to identify a line of best fit
    

Diagram of positive, negative and no correlation

• Correlation does not always indicate a relationship or causation  between two sets of variables so businesses need to conduct research to establish whether a relationship exists as well as the strength of that relationship
  

Line of best fit

• A line of best fit (regression line) is a visualisation of a correlation between two sets of data

  • It is drawn roughly through the middle of all of the points on a scatter diagram

  • The line may not go directly through any data points - but should have the same amount of data points above it as below it

    • A strong (positive or negative) correlation exists when data points sit close to the line of best fit

    • The further the distance between the line of best fit and the spread of data points, the weaker the (positive or negative) correlation 

• Where a line of best fit can be identified and when causation is determined, a business can extrapolate the data to make predictions around changes to either of the variables

  • E.g. extrapolation the line of best fit in the example below, the business could predict that employing seven sales managers would be result in likely sales of 46 units

• Extrapolation assumes that what has happened in the past will be the same as what will happen in the future
  

Diagram of a line of best fit

• Extrapolation works best when there is a strong correlation between the two data sets