8.1 Forecasting techniques - High low method & Linear regression

Question 1

Budgets are based on forecasts which might be prepared for:

Answer 1

• The volume of output and sales
• Sales revenue (sales volume and sales prices)
• Costs

Question 2

The purpose of forecasting is

Answer 2

• To establish realistic assumptions for planning in the budgeting process
• Might also be prepared on a regular basis for the purpose of feedforward control reporting

Question 3

Forecasts might be based on

Answer 3

• Simple assumptions such as prediction of a 5% growth in sales volume or an incremental approach to budgeted expenditure
• Or they could be prepared using a number of forecasting models, methods or techniques which might provide more reliable forecasts

Question 4

Forecast methods include

Answer 4

• The high-low method
• The uses of linear regression analysis
• Techniques of time series analysis

Question 5

Forecast methods are based on

Answer 5

• Data gathered from the budgeting process
  
  • Historic sales
  • Cost data
  • Economic data
  • Market research
• There is also a growing use of big data to support these other sources in spotting trends, identifying relationships between sets of data or in forecasting which costs may change in terms of behaviour in the future
• Forecasting can also be based on data plotted on a graph (scatter diagram) from which the line of best fit can be estimated (aim is to draw line through middle of data with the same slope as data)

Question 6

The high-low method formula

Answer 6

Total semi variable cost = Fixed cost + (Variable cost per unit x Activity level)

y = a + bx

y = total semi-variable cost
a = fixed cost
b = variable cost per unit
x = number of units produced

Question 7

Linear regression

Answer 7

• Is a more advanced calculation that takes into account all observations
• It uses a formula to estimate the linear relationship between the two variables
• This relationship can be used to make forecasts about the future

Question 8

Linear regression formula (equation of a straight line)

Answer 8

y = a + bx

y = dependent variable
a = intercept (on y-axis)
b = gradient
x = independent variable
n = number of pairs of data

This equation can be used for predicting values of y from a given x value

Question 9

The reliability of regression analysis depends on the

Answer 9

• Correlation which is the strength of the relationship between the two variables
• Two variables are said to be correlated if they are related to one another or more precisely if changes in the value of one tend to accompany changes in the other

Question 10

Degrees of correlation

Answer 10

• Perfectly correlated (more useful predictor): All pairs of values lie on a straight line and there is an exact linear relationship between the two variables (positive gradient = perfect positive correlation; negative gradient = perfect negative correlation)
• Partially correlated: Partial positive correlation = High values of x tend to be associated with high values of y and vice versa; Partial negative correlation = low values of x tend to be associated with high values of y and vice versa
• Uncorrelated - The values of the two variables seem to be completely unconnected

Question 11

Pearsonian correlation coefficient, r:

Answer 11

Measures the strength of the correlation, r must always be between -1 and +1

r = +1 There is a perfect positive linear correlation
r = 0 There is no linear correlation
r = -1 There is perfect negative linear correlation

Question 12

The coefficient of determination, r(squared)

Answer 12

• This measures how good the estimated regression equation is
• The higher the value the more confidence one can have in the regression equation
• Statistically it represents the proportion of the total variation in the y variable that is explained by the regression equation (remainder is accounted for by something else and is called the error term)
• It has range of values between 0 and 1

Question 13

Limitations of simple linear regression

Answer 13

• Assumes a linear relationship between the variables
• Only measures the relationship between two variables (in reality dependent variable is affected by many independent variables)
• Only interpolated (within range of original data) forecasts tend to be reliable (should not be used for extrapolation - outside of range)
• Regression assumes that the historical behaviour of the data continues into foreseeable future
• Interpolated predictions are only reliable if there is a significant correlation between the data
• It ignores inflation

Question 14

Adjusting forecasts for inflation

Answer 14

• When historical data is used to calculate a trend line or line of best fit, it should ideally be adjusted to the same index level for prices or costs. If the actual cost or revenue data is used without adjustments for inflation the resulting line or best fit will include the inflationary differences
• When a forecast is made from a line of best fit and adjustment to the forecast should be made for anticipated inflation in the forecast period