Simple Linear Regression (HL IB Business Management)

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

Diagram of a Typical Scatter Graph

An example of a scatter graph showing the number of sales managers employed by a business and the volume of Items sold

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

The main types of correlation between two variables

• 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

An example of a scatter graph with a line of best fit showing the number of sales managers employed by a business and the volume of items sold
 

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