Semi-Variable Costs
1 Introduction
The chapter relates to semi-variable costs i.e. part fixed and part variable. It may be necessary for you in the examination to identify the fixed and variable elements and in this chapter we will revise the ‘high-low’ method and also explain Regression Analysis.
2 High-Low Method
This is a quick and easy approach that estimates fixed and variable costs by comparing the highest and lowest activity levels.
Electricity costs for the first 6 months of the year are as follows:
Units produced | Cost ($) | ||
January | 340 | 2,260 | |
February | 300 | 2,160 | |
March | 380 | 2,320 | |
April | 420 | 2,400 | |
May | 400 | 2,300 | |
June | 360 | 2,266 |
Calculate the fixed and variable costs using the high-low method.
3 Problems with the high-low approach
4 Regression
If there is a reasonable degree of linear correlation between two variables, we can use regression analysis to calculate the equation of the best fit for the data.
This is known as least squares linear regression.
If the equation relating two variables, × and y, is
y = a + bx
then the values of a and b may be calculated using the following formulae (which are given in the examination)
The following table shows the number of units produced each month and the total cost incurred:
Units | Cost | ||
January | 100 | 40 | |
February | 400 | 65 | |
March | 200 | 45 | |
April | 700 | 80 | |
May | 600 | 70 | |
June | 500 | 70 | |
July | 300 | 50 |
Calculate the regression line, y = a + bx
5 Problems with regression analysis
6 The correlation coefficient
Pearson’s correlation coefficient is a measure of how linear the relationship between variables is.
A correlation coefficient of +1 indicates perfect positive linear correlation, whereas -1 indicates perfect negative linear correlation.
The further away from + or – 1, the less linear correlation exists.
The correlation coefficient may be calculated using the following formula (which is given to you in the examination)
Using the data in example 2, calculate the correlation coefficient
7 Coefficient of determination
The coefficient of determination is the square of the coefficient of correlation (r2).
It is a measure of how much of the variation in the dependent variable is ‘explained’ by the variation of the independent variable.
Semi-Variable Costs
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