Question Tag: Trend Analysis

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PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

Question

Some time ago, Robert launched a new product. Initially, sales were strong, but recent figures have raised concerns. Robert seeks a more accurate sales forecast to create detailed cash projections. The sales data below illustrates an underlying trend derived from an averaging method:

Year	Quarter	Trend Point (x)	Sales (Cartons) (y)
2016	3rd	1	10,000
2016	4th	2	10,760
2017	1st	3	10,920
2017	2nd	4	11,000
2017	3rd	5	11,050
2017	4th	6	11,080
2018	1st	7	11,085
2018	2nd	8	11,095
2018	3rd	9	11,120
2018	4th	10	11,130

On average, quarters 1 and 3 are 5% and 6% above the trend, respectively, while quarters 2 and 4 are 2% and 9% below it. Preliminary calculations for the 10 periods yield:

Linear Regression:
Slope: 82.67
Intercept: 10,472.33
Coefficient of determination: 0.535

Forecasting is needed for quarters 3 and 4 in 2019 and quarters 1 and 2 in 2020. There is a debate about using data from all 10 periods versus only the last 5. Analysis for the last five periods includes:

Results of last five periods‟ observations

(Note: y values are scaled down by 100 for ease of calculation.)

Required:
a. Forecast sales for the four quarters using the 10-period data. (8 Marks)
b. Prepare similar forecasts using the last five periods of data. (8 Marks)
c. Evaluate which data set provides the better forecast. (4 Marks)

Answer

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Tags: Coefficient of Determination, Linear Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Cost-Volume-Profit (CVP) Analysis
Series: MAY 2021

PM – May 2024 – L2 – SB – Q4 – Environmental and Social Performance Management

Forecast sales with seasonality adjustments and regression analysis to produce cash forecasts.

Question

Some time ago Robert launched a new product. At first, sales were good, but now the figures are causing concern. Robert wants a more accurate sales forecast to produce detailed cash forecasts.

Since there is some seasonality present in the raw data, the series for sales shown below represents the underlying trend based on an averaging process:

On average, quarters 1 and 3 are 5% and 6% respectively above trend, while quarters 2 and 4 are respectively 2% and 9% below trend.

Some preliminary calculations on the above ten observations have been carried out and the results are summarized below:

Required:
a. Forecast the sales for the next two years, adjusting for seasonality. (12 Marks)
b. Discuss the importance of seasonality adjustments in sales forecasting. (4 Marks)
c. Explain how Robert could use the sales forecasts to produce detailed cash forecasts. (4 Marks)

Answer

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Tags: Cash Forecasting, Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Environmental and Social Performance Management
Series: MAY 2024

PM – Nov 2021 – L2 – Q4 – Performance Measurement Systems

Adjust sales for seasonal variations and discuss deseasonalised data, along with the challenges of participative budgeting.

Question

You work as the assistant to the management accountant for Henry Limited, a medium-sized manufacturing company. One of its products, Product P, has been very successful in recent years, showing a steadily increasing trend in sales volumes. Sales volumes for the four quarters of last year were as follows:

Quarter	1	2	3	4
Actual sales volume (units)	420,000	450,000	475,000	475,000

A new assistant has recently joined the marketing department and she has asked you for help in understanding the terminology used in preparing sales forecasts and analysing sales trends. She said: “My main problem is that I do not see why my boss is so enthusiastic about the growth in Product P’s sales volume. It looks to me as though the rate of growth is really slowing down and has actually stopped in quarter 4. I am told that I should be looking at the deseasonalised or seasonally adjusted sales data, but I do not understand what is meant by this.”

You have found that Product P’s sales are subject to the following seasonal variations:

Quarter	1	2	3	4
Seasonal variation (units)	+25,000	+15,000	0	-40,000

Required:
a.
i. Adjust for the seasonal variations to calculate deseasonalised or seasonally adjusted sales volume (i.e., the trend figures) for each quarter of last year. (5 Marks)
ii. Assuming that the trend and seasonal variations will continue, forecast the sales volumes for each of the four quarters of next year. (4 Marks)

b. Explain what is meant by seasonal variations and deseasonalised or seasonally adjusted data. Indicate how they can be useful in analysing a time series and preparing forecasts. (5 Marks)

c. State the arguments for and challenges arising from managers participating in setting their budget targets. (6 Marks)

Answer

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Tags: Deseasonalisation, Participative Budgeting, Sales Forecasting, Seasonal Variations, Trend Analysis
Level: Level 2

Topic: Performance Measurement Systems
Series: NOV 2021

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

Question

The annual expenditures (N’000) of a family from 2000 to 2009 were as follows:

Year	Expenditure (N’000)
2000	600
2001	610
2002	580
2003	590
2004	480
2005	560
2006	550
2007	620
2008	490
2009	530

Required:
a. Setting year 2000 as $x = 0$ , fit the least squares line for the annual expenditures.
(15 marks)

b. Forecast what the expenditure will be in the years:
i. 2012 (2½ marks)
ii. 2016 (2½ marks)

Answer

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Tags: Expenditure, Forecasting, Least Squares, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

Question

A company takes stock for 5 months in each year. The stock figures of materials for the most recent three years are as tabulated below:

Determine the trend stock for month 6.

A. 84

B. 85

C. 86

D. 87

E. 88

Answer

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Tags: Forecasting, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

Question

Which of the following represents the types of variations in time series analysis?

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

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Tags: Time series, Trend Analysis, Variations
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

Question

The following methods are used to measure the trend of a time series EXCEPT:

A. Semi-average
B. Moving average
C. Free-hand
D. Deseasonalisation
E. Least squares

Answer

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Tags: Statistical Methods, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2015

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

Question

The figures given below are four years’ historical sales data of a company.

Required:
Calculate the moving averages, trends, and seasonal variations.

Answer

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Tags: Forecasting, Moving Averages, Seasonal Variations, Trend Analysis
Level: Level 1

Topic: Forecasting Techniques
Series: NOV 2023

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

Question

The monthly demand for maize (in hundreds of bags) for the last year in Bosua Market is shown below:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Demand	42	43	40	44	50	47	53	49	54	57	63	60

Required:
(a) Calculate the regression line $y = a + b x$ for the data. (9 Marks)

(b) Using the regression line in (a), determine the forecast for next year:
(i) January, (1 Mark)
(ii) February, (1 Mark)
(iii) March. (1 Mark)

Answer

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Tags: Demand forecast, Forecasting, Regression Analysis, Standard error, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

Question

Quarterly sales of a Golden Tree Chocolate Bar at a popular mall in KoKoLand City are given as follows:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	1260	756	588	1596
2	1352	966	579	2028
3	1786	920	865	2273

Required:
(i) Calculate the trend in the series using a 4-point centered moving average method. (4 Marks)

(ii) Using (i), calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis. (4 Marks)

(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data. (4 Marks)

(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model. (4 Marks)

Answer

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Tags: Additive model, Forecasting, Seasonal Variation, Time series, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

Question

Year	Quarter	Trend Point (x)	Sales (Cartons) (y)
2016	3rd	1	10,000
2016	4th	2	10,760
2017	1st	3	10,920
2017	2nd	4	11,000
2017	3rd	5	11,050
2017	4th	6	11,080
2018	1st	7	11,085
2018	2nd	8	11,095
2018	3rd	9	11,120
2018	4th	10	11,130

On average, quarters 1 and 3 are 5% and 6% above the trend, respectively, while quarters 2 and 4 are 2% and 9% below it. Preliminary calculations for the 10 periods yield:

Linear Regression:
Slope: 82.67
Intercept: 10,472.33
Coefficient of determination: 0.535

Results of last five periods‟ observations

(Note: y values are scaled down by 100 for ease of calculation.)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Linear Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Cost-Volume-Profit (CVP) Analysis
Series: MAY 2021

PM – May 2024 – L2 – SB – Q4 – Environmental and Social Performance Management

Forecast sales with seasonality adjustments and regression analysis to produce cash forecasts.

Question

Some time ago Robert launched a new product. At first, sales were good, but now the figures are causing concern. Robert wants a more accurate sales forecast to produce detailed cash forecasts.

Since there is some seasonality present in the raw data, the series for sales shown below represents the underlying trend based on an averaging process:

On average, quarters 1 and 3 are 5% and 6% respectively above trend, while quarters 2 and 4 are respectively 2% and 9% below trend.

Some preliminary calculations on the above ten observations have been carried out and the results are summarized below:

Answer

Find Related Questions by Tags, levels, etc.

Tags: Cash Forecasting, Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Environmental and Social Performance Management
Series: MAY 2024

PM – Nov 2021 – L2 – Q4 – Performance Measurement Systems

Adjust sales for seasonal variations and discuss deseasonalised data, along with the challenges of participative budgeting.

Question

Quarter	1	2	3	4
Actual sales volume (units)	420,000	450,000	475,000	475,000

You have found that Product P’s sales are subject to the following seasonal variations:

Quarter	1	2	3	4
Seasonal variation (units)	+25,000	+15,000	0	-40,000

b. Explain what is meant by seasonal variations and deseasonalised or seasonally adjusted data. Indicate how they can be useful in analysing a time series and preparing forecasts. (5 Marks)

c. State the arguments for and challenges arising from managers participating in setting their budget targets. (6 Marks)

Answer

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Tags: Deseasonalisation, Participative Budgeting, Sales Forecasting, Seasonal Variations, Trend Analysis
Level: Level 2

Topic: Performance Measurement Systems
Series: NOV 2021

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

Question

The annual expenditures (N’000) of a family from 2000 to 2009 were as follows:

Year	Expenditure (N’000)
2000	600
2001	610
2002	580
2003	590
2004	480
2005	560
2006	550
2007	620
2008	490
2009	530

Required:
a. Setting year 2000 as $x = 0$ , fit the least squares line for the annual expenditures.
(15 marks)

b. Forecast what the expenditure will be in the years:
i. 2012 (2½ marks)
ii. 2016 (2½ marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Expenditure, Forecasting, Least Squares, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

Question

A company takes stock for 5 months in each year. The stock figures of materials for the most recent three years are as tabulated below:

Determine the trend stock for month 6.

A. 84

B. 85

C. 86

D. 87

E. 88

Answer

Find Related Questions by Tags, levels, etc.

Tags: Forecasting, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

Question

Which of the following represents the types of variations in time series analysis?

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

Find Related Questions by Tags, levels, etc.

Tags: Time series, Trend Analysis, Variations
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

Question

The following methods are used to measure the trend of a time series EXCEPT:

A. Semi-average
B. Moving average
C. Free-hand
D. Deseasonalisation
E. Least squares

Answer

Find Related Questions by Tags, levels, etc.

Tags: Statistical Methods, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2015

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

Question

The figures given below are four years’ historical sales data of a company.

Required:
Calculate the moving averages, trends, and seasonal variations.

Answer

Find Related Questions by Tags, levels, etc.

Tags: Forecasting, Moving Averages, Seasonal Variations, Trend Analysis
Level: Level 1

Topic: Forecasting Techniques
Series: NOV 2023

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

Question

The monthly demand for maize (in hundreds of bags) for the last year in Bosua Market is shown below:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Demand	42	43	40	44	50	47	53	49	54	57	63	60

Required:
(a) Calculate the regression line $y = a + b x$ for the data. (9 Marks)

(b) Using the regression line in (a), determine the forecast for next year:
(i) January, (1 Mark)
(ii) February, (1 Mark)
(iii) March. (1 Mark)

Answer

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Tags: Demand forecast, Forecasting, Regression Analysis, Standard error, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

Question

Quarterly sales of a Golden Tree Chocolate Bar at a popular mall in KoKoLand City are given as follows:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	1260	756	588	1596
2	1352	966	579	2028
3	1786	920	865	2273

Required:
(i) Calculate the trend in the series using a 4-point centered moving average method. (4 Marks)

(ii) Using (i), calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis. (4 Marks)

(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data. (4 Marks)

(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model. (4 Marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Additive model, Forecasting, Seasonal Variation, Time series, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

Question Tag: Trend Analysis

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PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

PM – May 2024 – L2 – SB – Q4 – Environmental and Social Performance Management

Forecast sales with seasonality adjustments and regression analysis to produce cash forecasts.

PM – Nov 2021 – L2 – Q4 – Performance Measurement Systems

Adjust sales for seasonal variations and discuss deseasonalised data, along with the challenges of participative budgeting.

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

PM – May 2024 – L2 – SB – Q4 – Environmental and Social Performance Management

Forecast sales with seasonality adjustments and regression analysis to produce cash forecasts.

PM – Nov 2021 – L2 – Q4 – Performance Measurement Systems

Adjust sales for seasonal variations and discuss deseasonalised data, along with the challenges of participative budgeting.

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

QTB – May 2015 – L1 – SA – Q14 – Statistics

Identifying types of variations present in time series data.

QTB – May 2015 – L1 – SA – Q11 – Statistics

Identifying methods used to measure trends in time series data.

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

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