Least square lecture PDF

Preview

Summary

Download Least square lecture PDF

Description

Definition and explanation Least squares regression method is a method to segregate fixed cost and variable cost components from a mixed cost figure. It is also known as linear regression analysis. Least squares regression analysis or linear regression method is deemed to be the most accurate and reliable method to divide the company’s mixed cost into its fixed and variable cost components. This is because this method takes into account all the data points plotted on a graph at all activity levels which theoretically draws a best fit line of regression. Linear regression is basically a mathematical analysis method which considers the relationship between all the data points in a simulation. All these points are based upon two unknown variables; one independent and one dependent. The dependent variable will be plotted on the y-axis which is cost, and the independent variable will be plotted to the x-axis activity level which is on the graph of regression analysis. In literal manner, least square method of regression minimizes the sum of squares of errors that could be made based upon the relevant equation. The least squares regression method follows the same cost function as the other methods used to segregate a mixed or semi variable cost into its fixed and variable components. Let’s assume that the activity level varies along x-axis and the cost varies along y-axis. The following equation should represent the the required cost line: y = a + bx Where,    

y = total cost a = total fixed cost b = fixed cost, variable cost yata x = number of units

The values of ‘a’ and ‘b’ may be found using the following formulas.

The derivations of these formulas are not been presented here because they are beyond the scope of this website.

Example

For example, Master Chemicals produces bottles of a cleaning lubricant. The activity levels and the attached costs are shown below:

Required: On the basis of above data, determine the cost function using the least squares regression method and calculate the total cost at activity levels of 6,000 and 10,000 bottles. Solution

In our example:     

n=7 ∑x = 17,310 ∑y = 306,080 x2 = 53,368,900 xy = 881,240,300

We can find the values of ‘a’ and ‘b’ by putting this information in the above formulas: Computation of variable cost per unit (b):

The value of ‘b’ (i.e., per unit variable cost) is $11.77 which can be substituted in fixed cost formula to find the value of ‘a’ (i.e., the total fixed cost). Computation of total fixed cost (a):

1. Using the method of least squares, the cost function of Master Chemicals is: y = $14,620 + $11.77x 2. The total cost at an activity level of 6,000 bottles: y = $14,620 + ($11.77 × 6,000) = $85,240

3. The total cost at an activity level of 12,000 bottles: y = $14,620 + ($11.77 × 12,000) = $155,860

Limitations of least squares regression method: This method suffers from the following limitations: 1. The least squares regression method may become difficult to apply if large amount of data is involved thus is prone to errors. 2. The results obtained are based on past data which makes them more skeptical than realistic. High-low point method is a technique used to divide a mixed cost into its variable and fixed components. Sometimes it is necessary to determine the fixed and variable components of a mixed cost figure. Several techniques are used for this purpose such as scatter graph method, least squares regression method and high-low point method. On this page I will explain the use of high-low point method. Under high-low point method, an estimated variable cost rate is calculated first using the highest and lowest activity levels and mixed costs associated with them. This estimated variable cost rate is used to calculate total estimated variable cost included in the mixed cost figures at highest and lowest activity levels. The estimated variable cost is then subtracted from the total mixed cost figures at highest and lowest activity levels to find the fixed cost component. The cost function

Like scatter graph method and least squares regression method, high-low point method follows the following cost function (also known as cost volume formula): y = a + bx Where,    

y = total cost a = total fixed cost b = fixed cost x = number of units

To make the procedure simple and easy to understand , we can divide the calculations into the following three steps.

Steps involved in high-low point method Step 1 – calculation of variable cost rate:

The first step in high-low point method is to calculate an estimated variable cost rate. This rate is calculated by using the following formula:

Step 2 – calculation of variable cost component:

After calculating estimated variable cost rate, the second step is to calculate the total estimated variable cost at highest and lowest activity levels. It is calculated by multiplying the estimated variable cost rate (calculated in step 1) by highest and lowest activity levels. The formula is given below: Estimated total variable cost = Estimated variable cost rate × Highest or lowest level of activity Step 3 – calculation of fixed cost component:

The third and final step in high-low point method is to find out the fixed cost component of the total mixed cost. It is calculated by subtracting the estimated variable cost (calculated in step 2) from the total mixed cost figure. The formula for this purpose is given below: Fixed cost = Total mixed cost – Estimated total variable Advertisement: 0:05

Example: The Western Company presents the production and cost data for the first six months of the 2015.

Required: Determine the estimated variable cost rate and fixed cost using high-low point method. Also determine the cost function on the basis of data given above. Solution:

Variable cost rate (66,000 – 45,000)/(29,000 – 15,000) = $21000/14,000 = $1.5 per unit Variable cost:  

Highest activity level (May): 29,000 units × $1.5 = $43,500 Lowest activity level (January): 15,000 × $1.5 = $22,500

Fixed cost:  

Highest activity level (May): $66,000 – $43,500 = $22,500 Lowest activity level (January): $45,000 – $22,500 = $22,500

On the basis of data provided by Western Company, the cost function is: y = $22,500 + $1.5x The high-low point method uses only two data points (the highest and the lowest activity levels). Therefore, It is considered a less reliable method as compared to other methods available for mixed cost analysis....