ACCA SBL Syllabus G. Finance In Planning And Decision-Making - Linear Regression - Notes ^{7 / 8}

This model shows how dependent one variable is on another.

Eg. Marketing (X) and Sales (Y).

Sales is Dependent on Marketing Independent variable.

You would then need to determine the strength of the relationship between these two variables in order to forecast sales.

This is known as "The correlation"

Regression Equation


This helps us forecast

The formula for a simple linear regression is as follows:
Y = a + bx

where:

Y is the value we are trying to forecast (dependent)

“b” is the slope of the regression,

“x” is the value of our independent value, and

“a” The value of Y when the independent value is 0

A simpler way to picture this might be thinking of variable costs and fixed costs. 

We are trying to forecast TOTAL COSTS

So 
Y = Total costs
b = Variable cost per unit
a = Fixed Costs
x = Amount of units produced

In this graph, the dots represent the actual data

Linear regression attempts to estimate a line that best fits the data, and the equation of that line results in the regression equation

Covariance

• Direction

  If one variable increases and the other variable tends to also increase, then we experience positive covariance.

  If one variable increases and the other tends to decrease, then the covariance would be negative.

• 

• Correlation

  This is concerned with establishing how strong the relationship is:

  1. Perfect Correlation 

     refers to a correlation where all pairs of values lie on a straight line and there is an exact linear relationship between the two variables.

  2. Partial Correlation

     Not an exact relationship, but low values of (x) tend to be associated with low values of (y), and high values of (x) tend to be associated with high values of (y).

  3. No Correlation

     refers to a situation where the two variables seem to be completely unconnected

• Correlation Coefficient

  • The correlation calculation simply takes the covariance and divides it by the product of the standard deviation of the two variables.

• The degree of correlation can be measured (r).

  This gives a value of -1 and +1.  

  A correlation of +1 can be interpreted to suggest that both variables move perfectly positively with each other, and a -1 implies they are perfectly negatively correlated.

• 
Coefficient of Determination (r2)

  This measures how good the estimated regression equation is and is designated as r2 and has the range of values between 0 and 1.

  The higher the r2, the more confidence in the equation.

• Limitations of Simple Linear Regression Analysis

  • Assumes a linear relationship between variables;

    Measures only the relationship between two variables where in reality many variables exist;

    Assumes that the historical behaviour of the data continues into the foreseeable future;

    Interpolated predictions are only reliable if there is a significant correlation between the data.