Least Squares – NBC Institute

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 – 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

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

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:

(Total: 20 Marks)

Answer

Find Related Questions by Tags, levels, etc.

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

Topic: Forecasting
Series: NOV 2014

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

QT – Nov 2018 – L1 – Q6b – Forecasting

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

Question

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

Answer

Find Related Questions by Tags, levels, etc.

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

Topic: Forecasting
Series: NOV 2018

Question Tag: Least Squares

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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.

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.

QT – Nov 2018 – L1 – Q6b – Forecasting

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

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

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

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.

QT – Nov 2018 – L1 – Q6b – Forecasting

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

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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 – 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.

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QT – Nov 2018 – L1 – Q6b – Forecasting

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

You're reporting an error for "QT – Nov 2018 – L1 – Q6b – Forecasting"

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

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

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q4 – Forecasting"

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.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q3 – Statistics"

QT – Nov 2018 – L1 – Q6b – Forecasting

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

You're reporting an error for "QT – Nov 2018 – L1 – Q6b – Forecasting"

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