Quantitative Techniques for Forecasting

Question 1

High-Low Method – Estimating Relationships Between Variables

What is the purpose of the High-low method? (1)
What is the example used to illustrate the method? (3)
What is the formula used in the High-low method? (4)

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Answer 1

High-Low Method – Estimating Relationships Between Variables

What is the purpose of the High-low method?

• To predict the value of a dependent variable based on an independent variable

What is the example used to illustrate the method?

• Management accountant estimates supermarket checkout waiting time
• Waiting time is the dependent variable
• Number of customers is the independent variable

What is the formula used in the High-low method?

• y = a + bx
  
  • y: value of the dependent variable
  • x: value of the independent variable
  • a: part of y not dependent on x
  • b: change in y when x changes

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Question 2

Regression Analysis – Least Squares Method

What is regression analysis used for? (2)
What are the advantages of regression analysis over the high-low method? (2)

What are the limitations of regression-based forecasts? (4)

Answer 2

Regression Analysis – Least Squares Method

What is regression analysis used for?

• Calculating the line of best fit (y = a + bx)
• Alternative to the high-low method

What are the advantages of regression analysis over the high-low method?

• Uses all paired data to derive a definitive line of best fit
• Allows testing the reliability of forecasts by estimating correlation between variables

What are the limitations of regression-based forecasts?

• Not all relationships are linear
• Focusing on two variables may ignore relevant factors
• Caution is needed outside the relevant range – interpolation is more reliable than extrapolation
• The line of best fit may not have a high correlation

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Question 3

Correlation and Correlation Coefficient

What does it mean for two variables to be correlated? (1)
What does the correlation coefficient measure? (2)

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Answer 3

Correlation and Correlation Coefficient

What does it mean for two variables to be correlated?

• A change in one variable is accompanied by a change in the other

What does the correlation coefficient measure?

• The extent of linear correlation between two variables
• The value ranges from +1 to -1

r= +0.9955

Question 4

Cause and Effect and Rank Correlation

What does correlation describe? (1)
Does correlation imply causation? (1)
What does the rank correlation coefficient measure? (4)

Answer 4

Cause and Effect and Rank Correlation

What does correlation describe?

• How one variable moves alongside another

Does correlation imply causation?

• No, it does not prove that one variable causes the other to move

What does the rank correlation coefficient measure?

• Correlation between two sets of rankings
• Relationship between rankings rather than absolute values
• Useful when relative values matter more than absolute ones
• Uses Spearman’s rank correlation coefficient (Spearman’s Rho, ρ)

Question 5

Learning Effect – Conditions and Definitions

What does the learning curve effect refer to? (1)
What happens as the workforce gains experience? (1)
What is the impact of increased efficiency? (1)
Is the learning effect indefinite? (1)
What conditions are necessary for the learning effect to occur? (6)
What is the learning effect? (1)
What is the learning rate? (1)

Answer 5

Learning Effect – Conditions and Definitions

What does the learning curve effect refer to?

• Speeding-up of a job due to repetition

What happens as the workforce gains experience?

• Tasks are performed more quickly

What is the impact of increased efficiency?

• Labour costs and labour-driven costs are reduced over time

Is the learning effect indefinite?

• No, workers eventually reach a proficiency level that cannot be easily improved further

What conditions are necessary for the learning effect to occur?

• Significant manual element
• Repetitive tasks
• Early stage of production
• Consistency in the workforce
• No extensive breaks in production
• Motivation of the worker(s)

What is the learning effect?

• When cumulative total output doubles, the cumulative average time per unit falls to a proportion of its previous value

What is the learning rate?

• The proportion to which the cumulative average time per unit falls

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Question 6

Using the learning curve formula.
The learning curve formula can be used to calculate the cumulative average time per unit where the production volumes do not fit neatly into the “doubling” process.

Answer 6

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Question 7

Steady State and Standard Cost

When is the steady state reached in production? (1)
What happens once the steady state is reached? (2)
Why might the learning effect cease? (3)

Answer 7

Steady State and Standard Cost

When is the steady state reached in production?

• When further improvements in efficiency are not possible

What happens once the steady state is reached?

• Labour time per unit becomes a standard cost
• Standard cost is used for ongoing budgets

Why might the learning effect cease?

• Assumptions of learning curve theory no longer apply
• Lack of motivation to improve
• Machinery becomes the main driver of efficiency instead of labour

Question 8

Time Series Analysis

What is time series analysis? (2)
What is an example of time series analysis? (1)
What are the components of a time series? (2)
What types of variations exist in time series data? (3)

Answer 8

Time Series Analysis

What is time series analysis?

• A sequence of numbers, values, or measurements recorded against a timeline
• Allows observations and conclusions about how a variable behaves over time

What is an example of time series analysis?

• Monitoring sales quantities over days, weeks, or months to predict future sales

What are the components of a time series?

• Trend: The underlying, long-term movement over time
• Variations: Factors causing deviation from the trend

What types of variations exist in time series data?

• Seasonal variations: Short-term fluctuations due to timing in the planning cycle
• Cyclical variations: Recurring patterns over longer periods (e.g. economic cycles)
• Random variations: Irregular or unpredictable changes (e.g. pandemics, celebrity news)

Question 9

Time Series Models and Trend Estimation

What are the two models used to represent time series data? (2)
What is the trend in time series analysis? (1)
What methods are used to calculate and project the trend? (2)

Answer 9

Time Series Models and Trend Estimation

What are the two models used to represent time series data?

• Additive model: TS = Td + SV + (CV + RV)
  
  • Seasonal factors are numbers added/subtracted
  • e.g., +12, –5, +3
  • Seasonal effects are constant
  • Variability does not increase with the trend
  • Data is stable in amplitude
• Multiplicative model: TS = Td × SV × (CV + RV)
  
  • Seasonal factors are ratios around 1
  • e.g., 1.12, 0.95, 1.03
  • Seasonal effects scale with the level
  • Variability increases as the trend rises
  • Data behaves in percentages

What is the trend in time series analysis?

• A long-term general movement in the recorded values

What methods are used to calculate and project the trend?

• Regression analysis (using time periods as x and recorded values as y)
• Moving averages

Question 10

Illustration – establishing the trend and variations

The trend is established by taking a centred seven-point moving average
of the visitor numbers, for example: If we take Thursday as the middle day
of the week, our first weekly average is on the Thursday of the first week
and the trend value is the average for the whole of that week. As we move to the next day, the trend line is the average of the Tuesday of the first
week to the Monday of the second.
If we assume that any difference (variation) between the time series and
the trend is seasonal (i.e. based on the day of the week), then we can also
establish some estimated SVs.

Answer 10

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