Chapter 9 Flashcards
What is a scatter diagram/scatter graph
A Graph where y axis = dependent variable and x axis = independent variable (aka we change x to observe change in y)
-It is a good way of determining the relationship between two variables
WHat is the formula for a line of best fit?
Y= a + bX
Y= dependent variable
a = the y intercept
b= gradient of the line of best fit (steeper = higher)
X = the independent variable
What are the two main techniques for estimating the dependent variable?
1) High/Low method
2) Linear regression
What is the High/low method? (boring definition)
Official terminology
-A method of estimating cost behaviour by comparing the total costs associated with two different levels of output.
The difference in costs is assumed to be caused by variable costs increasing, allowing unit variable cost to be calculated.
-Following from this, since total cost is know, the fixed cost can be derived
What is high/low method (steps)
Step 1: Select the periods with the highest and lowest output and calculate the difference between them
—FInd Difference in Output and Difference in Total Costs
Step 2: Estimate the variable cost (VC) per unit
VC per unit = change in total cost/change in output
Step 3 Estimate the fixed cost (FC) by substitution
Total cost = Fixed Cost + Total Variable Cost
TC = FC + VC per unit*output aka Y =a +bx
–Find FC
Our cost relationship can then be summarised as:
TC = {FC} + {VCpU} x no of units
which can be used to forecast a future cost
What are the downfalls of the high/low method
ignoring all the middle data - which may scew actual line of best fit
What is another term for Linear regression
method of least squares?
What is linear regression used for?
Using linear regression it is possible to find the ‘line of best fit’ between two variables.
What is the line of best fit?
The line of best fit estimates the value of a and b in the linear equation
Y = a + bX
Where Y=total costs
X = output
a = y intercept = fixed costs
b = gradient = variable cost per unit
Using regression analysis, how can a be estimated
a = Y* - bX*
where Y * = the mean of Y values
where X * = the mean of X values
Using regression analysis, how can b be estimated?
b = n SUMxy - (SUMx)(SUMy)/
n SUMx^2 -(SUMx)^2
where n = the number of pairs of data
What is the correlation coefficient?
The CC indicates the strength of the realtionship between the variables
aka (how close the line of best fit is to the actual variables)
symbol = r - always inbetween -1 and +1.
The sign of r indicates the gradient of the ‘best fit’ line.
-the closer the cc is to +-1, the closer the line of best fir is to the actual variables
1= perfectly straight line
What is the correlation coefficient formula?
Need to know
The linear function you want to present as your answer?
Total cost = N + NX
What is the coefficient of determination?
The CD indicates the proportion of change in the y (dep)(aka costs) variable which is explained by change in the x (indep)(aka output) variable
r^2
The CD will always be somewhere between 0 and +1
in simple terms: It indicates that N% of the change in the total cost is explained by the change in the output
and hence (100-N)% of the change is due to other factors