1. Paper F2 Management Accounting
2018/12/6

2. Chapter 14 Forecasting
2018/12/6

3. Forecasting Chapter Preview Cost estimation Sales forecast
Regression analysis
Time series analysis
Index
Product life cycle
2018/12/6
Ji Weili, JXUFE

4. Costs vs output - scattergraph$
output
y = a + bx
(y)
dependent variable
We are going to look at two techniques to determine the equation y=a+bx – use same example for both techniques
(x)
independent variable
2018/12/6
Ji Weili, JXUFE

5. Correlation Definition Degrees of correlation
perfectly、partly、 uncorrelated
完全相关、部分相关、不相关
Positive and negative correlation
正相关和负相关
2018/12/6
Ji Weili, JXUFE

6. Correlation coefficient(相关系数）
r = nxy - xy
([n(x2) - (x)2][n(y2) - (y)2])
-1≤r≤+1
r = +1
- perfect positive correlation
Point out the similarity with the equation for b and show with numbers how you can do the calculation quickly using data from the previous example
r = -1
- perfect negative correlation
r = 0
- no correlation
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7. Example: the correlation coefficient
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8. Correlation coefficient
Exam focus point
The formula for the correlation coefficient is given in the exam.
Note: time series(时间序列）--X represents the period of time
2018/12/6
Ji Weili, JXUFE

9. Correlation coefficient
Question
Sales of product A between 20X7 and 20Y1 were as follows.
Required
Determine whether there is a trend in sales. In other words, decide whether there is any correlation between the year and the number of units sold.
2018/12/6
Ji Weili, JXUFE

10. Coefficient of determination（可决系数）
The amount of variation in y which appears to be explained by variation in x
Does NOT prove “cause and effect”
Coefficient of determination = r2
Note：Identify correlation and causation
(相关关系和因果关系)
2018/12/6
Ji Weili, JXUFE

11. Linear regression Finds the mathematical line of best fit
Linear regression analysis (Least square method)--On a scatter diagram by minimising the distance of the points from the line.
线性回归分析（最小二乘法或最小平方法）
Given in exam
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12. Example: the least squares method
Linear regression
Formulae:
y = a + bx
b = nxy - xy
nx2 - (x)2 P
Example: the least squares method
a = y - b x
n n
Given in exam
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13. Reliability of regression analysis forecasts
Assumes linearity between X and Y
The observation used may be atypical
Historic data is used and patterns may change in future
The amount of data available is very important
Extrapolation is less reliable than interpolation
2018/12/6
Ji Weili, JXUFE

14. Quick quiz
1. Which of the following correlation coefficients indicates the strongest relationship between two variables?
A B C – 0.2 D – 1.0
2. The correlation coefficient (r) for measuring the connection between two variables (x and y) has been calculated as 0.6.
How much of the variation in the dependent variable (y) is explained by the variation in the independent variable (x)?
A 36% B 40% C 60% D 64%
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Ji Weili, JXUFE

15. Quick quiz
3. The following statements relate to the calculation of the regression line y = a + bx using the information on the formulae sheet at the end of this examination paper:
(i) n represents the number of pairs of data items used
(ii) (Σx)2 is calculated by multiplying Σx by Σx
(iii) Σxy is calculated by multiplying Σx by Σy
Which statement(s) is/are correct?
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16. Time series（时间序列）
A time series is a series of figures or values recorded over time.
Regression can be used to find a trend line.
The components of time series
A time series
Random variations
A trend
Seasonal variations
Cyclical variations
2018/12/6
Ji Weili, JXUFE

17. Trend values can be determined by a process of moving averages.
Finding the trend
Trend values can be determined by a process of moving averages.
To remove seasonal or cyclical variations from a time series by a process of averaging.
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Ji Weili, JXUFE

18. Example: moving average
Ⅰ. an odd number of time period
Moving average of 3 years
410
430
460
453
470
Sales
390
380
460
450
470
440
500
Year 1 2 3 4 5 6 7
Trend
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19. Example: moving average
Ⅱ. an even number of time period
Mid-point of 2 moving average
650
657.5
660
662.5
Year 1 2 3 4 5 6 7 8
Sales
600
840
420
720
640
860
740
Moving average of 4 years
645
655
660
665
Trend
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20. Finding the seasonal variations
Ⅰ.Additive model
step1:calculate seasonal variation=actual result - trend figue
step 2: average these variations
step 3: revise the variations--make sure the final total of the variations sum to zero
step 4: forecast figue=trend + seasonal variation
Example:P
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21. Ⅱ.Multiplication model
step1:calculate seasonal variation=actual result / trend figue
step 2: average these variations
step 3: revise the variations--make sure the final total of the variations sum to 4
step 4: forecast figue=trend* (1+seasonal variation)
2018/12/6
Ji Weili, JXUFE

22. Quick quiz
An additive time series has the following trend and seasonal variations:
Trend Y = 4, X
Where
Y = sales in units
X = the number of quarters, with the first quarter of 2014 being 1, the second quarter of 2014 being 2 etc.
Seasonal variation
Quarter
Quarterly variation (units) –4 –
What is the forecast sales volume for the fourth quarter of 2015?
A 4, B 4, C 4, D 4,053
2018/12/6
Ji Weili, JXUFE

23. Using index numbers（指数）
price indices & quantity indices
Laspeyre indices(拉氏指数）--权数固定在基期
P2Q1/P1Q1 1-基期 2-报告期
Paasche indices（派氏指数）--权数固定在报告期
P2Q2/P1Q2
用一篮子固定产品计算的物价指数成为拉氏指数如CPI，把用一篮子可变产品计算的称为派氏指数如GDP平减指数
Fisher ideal indices（费雪指数）--拉氏指数和派氏指数的几何平均数
RPI 商品零售价格指数 CPI 居民消费价格指数
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24. Quick quiz
1.Four yeas ago material X cost $5 per kg and the price index most appropriate to the cost of material X stood at 150.The same index now stands at 430.What is the best estimate of the current cost of material X per kg?
A $1.74($5×150÷430)
B $9.33($5×(430－150)÷150)
C $14.33($5×430÷150)
D $21.50($5×430÷100)
2018/12/6
Ji Weili, JXUFE

25. Quick quiz 2.The following data relates to a company’s overhead cost.
Time Output Overhead cost Price
(units) ($) index
2 years ago 1, ,
current year 3, ,
Using the high low technique, what is the variable cost per unit (to the nearest $0.01) expressed in current year prices?
A $3.22
B $4.13
C $4.65
D $5.06
2018/12/6
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26. Sales forecasting: the product life cycle
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27. End of Chapter 14
2018/12/6
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