Linear Regression

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Linear Regression

This model says how dependent one variable is on another.

For example cost (X) and volume (Y).

These variables are called the dependent and independent variables.

The Dependent variable’ value depends on the value of the other variable.

E.g. Sales may be dependent on marketing spend

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

For example, if the marketing budget increases by 1%, how much will your sales increase?

Regression Equation


This helps us predict the variable we require. 


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” represents the y-intercept. (the value we are trying to 
forecast 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 date. 

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

Once a linear relationship is identified and quantified using linear regression analysis, values for (a) and (b) are obtained and these can be used to make a forecast for the budget such as a sales budget or cost estimate for the budgeted level of activity

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