Chapter 9

Question 1

What is a scatter diagram/scatter graph

Answer 1

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

Question 2

WHat is the formula for a line of best fit?

Answer 2

Y= a + bX

Y= dependent variable
a = the y intercept
b= gradient of the line of best fit (steeper = higher)
X = the independent variable

Question 3

What are the two main techniques for estimating the dependent variable?

Answer 3

1) High/Low method
2) Linear regression

Question 4

What is the High/low method? (boring definition)

Answer 4

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

Question 5

What is high/low method (steps)

Answer 5

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

Question 6

What are the downfalls of the high/low method

Answer 6

ignoring all the middle data - which may scew actual line of best fit

Question 7

What is another term for Linear regression

Answer 7

method of least squares?

Question 8

What is linear regression used for?

Answer 8

Using linear regression it is possible to find the ‘line of best fit’ between two variables.

Question 9

What is the line of best fit?

Answer 9

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

Question 10

Using regression analysis, how can a be estimated

Answer 10

a = Y* - bX*

where Y * = the mean of Y values
where X * = the mean of X values

Question 11

Using regression analysis, how can b be estimated?

Answer 11

b = n SUMxy - (SUMx)(SUMy)/
n SUMx^2 -(SUMx)^2

where n = the number of pairs of data

Question 12

What is the correlation coefficient?

Answer 12

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

Question 13

What is the correlation coefficient formula?

Answer 13

Need to know

Question 14

The linear function you want to present as your answer?

Answer 14

Total cost = N + NX

Question 15

What is the coefficient of determination?

Answer 15

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

Question 16

What are the limitations of linear regression?

Answer 16

1) Assumes a linear relationship between x and y

2) It only measures the relationship between the two variables d
In reality the dependent variables could be affected by many independent variables

3) Only those forecasts within the data set tend to be reliable.
The equation should not be used for extrapolation outside the data set.

4) Historical data is not necessarilt a good indicator of future events

Question 17

What should spearmans rank correlation coefficient be used

Answer 17

R
-When you want to measure the order or rankings of data rather than their actual values
Its value can range from -1 to +1
A RCC close to +1 demonstrates a very strong relationship between the order of results of one distribution with the order of results from anothe distribution

Question 18

What is the formula for speamans rank correlation?

Answer 18

Formula for rank correlation is given on the formulae sheet
d = difference in order between a pair of rankings
n = the number of pairs of data

NB: If items are ranked equally, then the average position is used
aka if 2nd and 3rd are equal - they would both be ranked 2.5

Question 19

What is a time series?

Answer 19

TS - a set of data observed over a period of time

e.g. sales patterns by day, by week, by month, by year

Question 20

WHat is a time series forecast?

Answer 20

It identifies four components from a series of past figures recorded over time and then uses them to forecast the future.
These components are
-Tren
-Seasonal Variation
-Cyclical Variation
-Random Variation

Question 21

TS forecast: What is the trend component?

Answer 21

The underlying long-term movement over time in historic data. This can be determined by a process of moving averages.
general upward trend in house prices over the last five years

Question 22

TS forecast: What is Seasonal variation

Answer 22

short-term periodic fluctuations in historic data. This can be determined by using either the additive or the proportional models

e.g. ice cream higher in summer than winter

Question 23

TS forecast: What is seasonal variation?

Answer 23

longer-term fluctuations caused by such factors as economic activity or economic cycles

Question 24

TS forecast: What is random variation?

Answer 24

unpredictable fluctuations such as an act of nature

Question 25

What are the two models that we can use to determine the forecast time series?

Answer 25

The additive model
-The multiplicative (or proportional) model

Question 26

What is the additive model?

Answer 26

USed where the components are assumed to add together to give the time series.
The components of the time series are quoted in actual (absolute) terms/values

**EXAM example
trend eqn for forecasting sales (A) for quarter (B) is A = N +NB

Q3 has a seasonal adj factor of +1.6 using additive model. What is the time series forecast for Q3
TS (sales forecast for Q3 = N+N(3) +1.6

Question 27

What is the multiplicative model

Answer 27

used where the components are considered as multiplying together to give the TS
The components of the TS are quoted as a % or fraction of the trend

TS = T*S

Question 28

What is the difference between the additive model and the multiplicative model?

Answer 28

The additive model assumes that the seasonal variations are independent of the trend
The multiplicative model assumes the seasonal variations are linked to the size of the trend

Question 29

What are the three ways of determining the trend in the above data?

Answer 29

1) Preparing a graph
2) Moving averages
3) Linear regression

Question 30

Preparing a graph method

Answer 30

Using the data to construct a time-series graph
- can put a line of best fit
extrapolate going forward
add seasonality but addition or multiplicative model

Question 31

Moving averages?

Answer 31

step 1: Decide how many periods to include in the average
-four-quarter range or 7 day range etc.
step 2: work out the averages
-any seasonal distortions should be eliminated, leaving us with an estimation of the underlying trend
step 3 centre moving averages
step 4 seasonal variation
step 5 forecast

1st column: Per question
2nd - moving average
3rd Centred moving average (T)
Line up data with Q3/Q4 etc by making smaller averages between two
4th Seasonal variation
-found by TS-T or TS/T

Question 32

Moving averages: how to calculate average quarterly increase?

Answer 32

use centred moving average
number of jumps = N
total gap/N = average quarterly increase

Add this onto the final value again and again to forecast the centred moving average

Then factor in seasonal allowance - average Q1 values and add/multiply to centreed moving average for total sales (TS)

Question 33

Linear regression technique

Answer 33

Year |quarter |period(x) |sales (y) |(Xy) |X2)

nb period of Year 2 Q1 = 5 etc

linear regression to produce

y= N+Nx
These figures then need to be adjusted for seasonal variations either using the additive or multiplicative models

Question 34

What are the limitations of forecasting?

Answer 34

-Assumes the historic trends will continue into the future (for TS analysis)
-Becomes less reliable if you go outside the ranges of existing observations
-Seasonal variations may not be consistent into the future
-Assumes there is an identifiable relationship