Topic: Forecasting

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

Question

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2005	22	35	82	37
2006	24	46	81	44
2007	25	40	87	49
2008	29	42	100	55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

Answer

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Tags: Least Squares, Sales Forecasting, Time series, Trend Estimation
Level: Level 1

Topic: Forecasting
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q6 – Forecasting

Identifies the method that is not considered a quantitative forecasting technique.

Question

The following are quantitative techniques of forecasting in business analysis EXCEPT:
A. Regression analysis
B. Delphi method
C. Moving average
D. Exponential smoothing
E. Time series analysis

Answer

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Tags: Business Analysis, Forecasting, Quantitative Techniques
Level: Level 1

Topic: Forecasting
Series: NOV 2014

QT – Nov 2017 – L1 – Q3 – Forecasting

Analyze the relationship between website hits and promotions using correlation and regression analysis.

Question

A small business is interested in the relationship between the number of hits on its website (measured by the number of visitors that have used the main menu) and the level of website promotion (in GH¢ 00s). The table below gives the figures for the last six months:

Month	Web Site Hits	Web Site Promotion (GH¢ 00s)
1	25	1.0
2	24	1.2
3	56	1.6
4	54	1.4
5	55	1.2
6	58	1.8

Required:
a) Graph the number of website hits against website promotion. (2 marks)
b) Comment on any possible relationship in (a) above. (2 marks)
c) Calculate the correlation coefficient and give an interpretation to its value. (5 marks)
d) Determine the regression line. (5 marks)
e) Using the regression line found in part (d) above, predict the number of website hits if the level of monthly promotion were increased to GH¢200. (2 marks)
f) Comment on the reliability of your prediction in (e) above. (1 mark)
g) Comment on the simple forecasting model you have developed above. (3 marks)

Answer

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Tags: Correlation Coefficient, Forecasting, Regression Line
Level: Level 1

Topic: Forecasting
Series: NOV 2017

QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

Question

The number of enquiries being made to a mail order business during a Monday to Friday working week is given as:

Week	Monday	Tuesday	Wednesday	Thursday	Friday
1	34	36	24	25	41
2	33	34	24	23	43
3	35	37	25	25	47

Required: i) Plot the data on a graph.
ii) Compute a 5-period moving average for the data.
iii) Compute a ‘weighted’ moving average for the data if the smoothing constant is $α = 0.5$ .
iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.
v) Comment on the suitability of the two smoothing methods above. (16 marks)

Answer

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Tags: Data Plotting, Forecasting, Moving Averages, Time series, Weighted Moving Averages
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

Question

The objective of smoothing methods is to smooth out the random variations due to irregular components of the time series and provide an overall impression of the pattern of movement in the data over time.

Required:
Explain the following smoothing methods:

i) Moving averages (2 marks)
ii) Exponential smoothing (2 marks)

Answer

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Tags: Exponential Smoothing, Forecasting, Moving Averages, Smoothing Methods, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

Question

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
1	75	70	75	80
2	95	85	80	65
3	100	105	115	90

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method. (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations. (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data. (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model. (6 marks)

Answer

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Tags: Forecasting, Moving Averages, Multiplicative Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

Question

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly:

Food (x)	10	12	14	16	18	20	22	24	26	28
TroTro (y)	25	24	22	20	19	17	13	12	11	10

Required:

a) Using a graph paper, construct a scatter diagram of the data.
(4 marks)

b) Determine the correlation coefficient.
(4 marks)

c) Calculate the coefficient of determination of the data and interpret its value.
(4 marks)

d) Determine the regression line of $y$ on $x$ , and interpret the coefficient.
(8 marks)

Answer

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Tags: Coefficient of Determination, Correlation Coefficient, Regression Line, Scatter Diagram
Level: Level 1

Topic: Forecasting
Series: MAY 2017

QT – May 2016 – L1 – Q2 – Forecasting

This question asks for the creation of a linear regression trend equation, seasonal components, and forecasts for chocolate sales.

Question

Countess Company trades in bars of Golden Tree Chocolate from Tema Cocoa Processing Company Limited. The number of bars of chocolate sold per quarter over a four-year period by Countess Company is:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	20	10	4	11
2	33	17	9	18
3	45	23	11	25
4	60	30	13	29

Required:

i) Plot the data on a graph (3 marks)

ii) Calculate a linear regression trend equation for the data (5 marks)

iii) Calculate the four seasonal components using a multiplicative model (5 marks)

iv) Forecast the number of bars of chocolate for the next two years (5 marks)

v) Comment on the reliability of the forecasts in iv) above (2 marks)

Answer

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Tags: Forecasting, Linear Regression, Multiplicative Model, Seasonal Components, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2016

QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

Question

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. The mean number of absentees per day for each quarter of the years 1999 to 2001 and Quarter 1 in 2002 is given in the table below:

	Q1	Q2	Q3	Q4
1999	25.10	14.40	9.50	23.70
2000	27.90	16.90	12.40	26.10
2001	31.40	19.70	15.90	29.90
2002	34.50	–	–	–

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures. (3 marks)

b) Using the method of 2-quarterly centered moving averages,
i) Determine the trend in the series and superimpose this on your graph in (a). (4 marks)
ii) Determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i). (3 marks)

c) Using an appropriate decomposition model, determine the seasonal variations in the data. Give reasons for your choice of model. (5 marks)

d) Use your analysis above to roughly forecast the mean number of absentees for the remaining quarters of 2002. Comment on your forecast. (5 marks)

Answer

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Tags: Absenteeism, Forecasting, Seasonal Variations, Time series, Trend
Level: Level 1

Topic: Forecasting
Series: NOV 2016

QT – Nov 2016 – L1 – Q3 – Forecasting

Derive a regression forecasting equation for iron rod demand based on construction permits and analyze the results.

Question

The Branch Manager of a building material production plant feels that the demand for iron rod shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:

Construction Permits	Iron Rods
15	6
9	4
40	16
20	6
25	13
25	9
15	10
35	16

Required:

i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data. (9 marks)
ii) Interpret your regression coefficient in (i) above. (1 mark)
iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30. (2 marks)
iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer. (2 marks)
v) Calculate the coefficient of determination and interpret it. (6 marks)

Answer

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Tags: Construction Permits, Forecasting, Iron Rods, Regression
Level: Level 1

Topic: Forecasting
Series: NOV 2016

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

Question

The secretariat of an association of industries gathered the following data from a random sample of member firms that produce similar products:

Required:
i) Compute the Pearson’s product moment correlation coefficient for the data. (6 marks)
ii) Hence, compute the coefficient of determination. (2 marks)
iii) Comment on your answer in (ii). (2 marks)
iv) Compute Spearman’s rank correlation coefficient for the data and comment on your answer. (8 marks)

Answer

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Tags: Coefficient of Determination, Correlation, Pearson Correlation, Ranking, Spearman Correlation
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – May 2018 – L1 – Q7a – Forecasting

Sketch scatter graphs for perfect positive and negative correlation.

Question

Sketch a scatter graph for two variables (dependent and independent variables) that represents:
i) Perfect positive correlation between the variables. (1 mark)
ii) Perfect negative correlation between the variables. (1 mark)

Answer

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Tags: Correlation, Negative Correlation, Positive Correlation, Scatter Plot
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

Question

a) The quarterly unit sales of electronic items of a retail company for the last three years are as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2013	100	115	70	210
2014	120	165	100	220
2015	150	195	120	270

Required:
i) Calculate a centered three-moving average of the unit sales. (3 marks)
ii) Calculate the trend using a centered four-quarterly moving average. (4 marks)
iii) Calculate the four seasonal variations using (ii) and the multiplicative model. (7 marks)
iv) Forecast the number of unit sales for the year 2016 using the multiplicative model. (4 marks)
v) Comment on your answer in (iv). (2 marks)

Answer

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Tags: Forecasting, Moving Averages, Seasonal Variations, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – May 2018 – L1 – Q2 – Forecasting

Develop a regression model for energy consumption based on temperature and calculate the standard error of estimate.

Question

A Ghanaian student studying abroad wants to develop an empirical model for energy consumption (in kilowatts per day) as a function of the daily high temperature (in degrees Celsius) in winter. For nine days the following information was obtained:

Temperature (°C)	-0.4	-0.2	0.3	0.8	1.1	1.4	1.8	2.1	2.5
Energy used (kW)	28	30	26	25	26	26	27	26	22

Required:
a) Identify the response and predictor variables, based on the purpose for developing the regression model. (2 marks)
b) Determine the coefficient of regression and the regression constant. Give your values to 2 decimal places. (5 marks)
c) Interpret your results in b) above. (3 marks)
d) Write the equation of the regression line of energy use on temperature in the form $y = a + b x$ . (2 marks)
e) Estimate the student’s daily energy consumption when the daily high temperature is 2 degrees Celsius. (2 marks)
f) Determine the standard error of estimate. (6 marks)

Answer

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Tags: Energy Consumption, Regression, Standard Error of Estimate, Temperature
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

Question

Membership of Pro Amalion, a network of professional volunteers, has grown over the years but in the months of the second quarter, there was always a decline. The table below shows membership records for a period of four years:

Year	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Year 1	713	694	735	755
Year 2	767	733	766	780
Year 3	787	755	798	814
Year 4	816	790	826	843

Required:
i) Calculate the centered four-quarterly moving average of membership. (4 marks)
ii) Using a least squares trend equation based on (i) above, calculate the trend values. (5 marks)
iii) Using (ii) above, calculate the percentage seasonal variation and the average seasonal variation of membership. (5 marks)
iv) Determine the seasonally adjusted forecast of membership for each of the four quarters of Year 5. (4 marks)

Answer

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Tags: Forecasting, Least Squares, Membership Forecast, Moving Averages, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2018 – L1 – Q6a – Forecasting

State the two main models of time series analysis.

Question

State the TWO (2) main models of time series analysis. (2 marks)

Answer

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Tags: Additive model, Forecasting, Models, Multiplicative Model, Time series
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2018 – L1 – Q1b – Forecasting

Determine the number of errors a student would make after 280 minutes of study and the expected change in errors for a 1-minute change.

Question

The study time in minutes and the number of errors on a mock examination paper made by ten (10) ICAG students are given below:

Student	1	2	3	4	5	6	7	8	9	10
Study Time (X)	90	100	130	150	180	200	220	300	350	400
Errors (Y)	25	28	20	20	15	12	13	10	8	6

(i) Determine how many errors a student would make in the examination if he studied for 280 minutes.

(ii) Determine the expected change in the number of errors if there is a 1-minute change in study time.

Answer

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Tags: Errors Prediction, Regression Analysis, Study Time
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2018 – L1 – Q1a – Forecasting

Explain the term coefficient of correlation in forecasting.

Question

Explain the term Coefficient of Correlation in forecasting.

Answer

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Tags: Coefficient of Correlation, Forecasting, Regression
Level: Level 1

Topic: Forecasting
Series: NOV 2018

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

Topic: Forecasting

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

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QTB – Nov 2014 – L1 – SA – Q6 – Forecasting

Identifies the method that is not considered a quantitative forecasting technique.

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QT – Nov 2017 – L1 – Q3 – Forecasting

Analyze the relationship between website hits and promotions using correlation and regression analysis.

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QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

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QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

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QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

You're reporting an error for "QT – May 2019 – L1 – Q1a – Forecasting"

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

You're reporting an error for "QT – May 2017 – L1 – Q7 – Forecasting"

QT – May 2016 – L1 – Q2 – Forecasting

This question asks for the creation of a linear regression trend equation, seasonal components, and forecasts for chocolate sales.

You're reporting an error for "QT – May 2016 – L1 – Q2 – Forecasting"

QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

You're reporting an error for "QT – Nov 2016 – L1 – Q7 – Forecasting"

QT – Nov 2016 – L1 – Q3 – Forecasting

Derive a regression forecasting equation for iron rod demand based on construction permits and analyze the results.

You're reporting an error for "QT – Nov 2016 – L1 – Q3 – Forecasting"

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

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QT – May 2018 – L1 – Q7a – Forecasting

Sketch scatter graphs for perfect positive and negative correlation.

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QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

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QT – May 2018 – L1 – Q2 – Forecasting

Develop a regression model for energy consumption based on temperature and calculate the standard error of estimate.

You're reporting an error for "QT – May 2018 – L1 – Q2 – Forecasting"

QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

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QT – Nov 2018 – L1 – Q6a – Forecasting

State the two main models of time series analysis.

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QT – Nov 2018 – L1 – Q1b – Forecasting

Determine the number of errors a student would make after 280 minutes of study and the expected change in errors for a 1-minute change.

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QT – Nov 2018 – L1 – Q1a – Forecasting

Explain the term coefficient of correlation in forecasting.

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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.

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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.

You're reporting an error for "QT – Nov 2015 – L1 – Q1b – Forecasting"

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