M451 FORECASTING PRACTICE QUESTIONS1. Discuss what is meant by the term ‘forecasting’ and any factors that need tobe taken into account when undertaking any forecasting.2. Discuss/explain possible types of qualitative forecasting.3. With the advent of more computer processing power and the ability to processlarge amounts of data, another type of forecasting/predictive method isbecoming increasingly popular. Describe this method.4. Previous demand for a product is: MonthDemand142002430034000444005500064700753008490095400105700116300126000 Plot this data on a graph, together with the associated regression line. Givethe estimated forecasted demand for months 14 and 18 and discuss which ofthese forecasts is the most reliable figure. State whether time seriesforecasting could have been used in this situation? If so, why might youchoose to use linear regression?5. A company periodically offers a product at special prices. Historicalobservations are shown below: Price, £Sales2.707603.505102.009804.202503.103204.05480 Plot this data on a graph, together with the associated regression line. Givethe estimated forecasted sales for prices of £2.50 and £5.00 and discusswhich is the most reliable figure. State whether time series forecasting couldhave been used in this situation. If so, why might you choose to use linearregression?6. A company has a demand history as below: DayDemand12202240323042405260625072308– Calculate forecasts for weeks 5 to 8 using(a) SMA4 (simple moving average)(b) WMA (weighted moving average), with weights 0.4, 0.3, 0.2 and 0.1, with0.4 being the most recent demand value.(c) SES (single exponential smoothing), using 𝛼𝛼 = 0.15 and F4 as 235(d) TAS (trend adjusted exponential smoothing), using 𝛼𝛼 = 0.2, 𝛽𝛽 = 0.3, A3 as230 and T3 as 0.Also, calculate the MAPE (mean absolute percentage error) for each of themethods and say what your result indicates.7. Over a period of three years, a company experiences sales as shown: QuarterYear 1Year 2Year 3130003300350221700210024483900150017684440051005882 a) Calculate an average seasonal index for each quarter.b) If the aggregate demand for year 4 is expected to be 14,800 forecast thesales figures for each quarter of the year.c) Suggest how the forecast might be improved.d) Deseasonalise the data and plot the values along with the original demanddata.e) Looking at your plot, what can you say about the pattern that you see?SAMPLE SOLUTIONSNOTE THAT ALTHOUGH SOLUTIONS HERE HAVE BEEN COMPLETED USINGEXCEL, FOR ANY CALCULATIONS IN THE EXAM YOU SHOULD SHOW YOURHANDWRITTEN CALCULATIONS. ANY PLOTS SHOULD ALSO BE COMPLETEDBY HAND. COMMENTS ARE INDICATIVE ONLY AND NOT EXHAUSTIVE.1. 2. 3. See forecasting lecture 1 slides (Forecasting introduction andqualitative methods).4. Previous demand for a product is: MonthDemand142002430034000444005500064700753008490095400105700116300126000 Plot this data on a graph, together with the associated regression line. Youshould plot the graph by hand and find the regression line, r and R2 using yourcalculator. The values you will find are A = 3766.666667, B = 192.3076923, r =0.9375332937 and R2 = 0.8789686738, although all these decimal places are notrequired. Give the estimated forecasted demand for months 14 (F14=192.31(14)+3766.67=6459.01) and 18 (F18 =192.31(18)+3766.67=7228.25) anddiscuss which of these forecasts is the most reliable figure (F14 as it is less into thefuture). State whether time series forecasting could have been used in thissituation? Yes, although you would need to account for trend. If so, why mightyou choose to use linear regression? E.g. Given the values of r and R2, thereappears to be a strong causal relationship and the trend is linear. Once have aregression line, simple to make predictions. Strong r/R2 indicates could trustforecasts in shorter term. As always further forward is less reliable.5. A company periodically offers a product at special prices. Historicalobservations are shown below: Price, £Sales2.707603.505102.009804.202503.103204.05480 Plot this data on a graph, together with the associated regression line. From yourcalculator you will find A = 1454.604462, B = -277.627968, r = -0.8433929183and R2 = 0.7113116147, although all these decimal places are not required Givethe estimated forecasted sales for prices of £2.50 (1454.60-277.63(2.50) = 761)and £5.00 (1454.60-277.63(5.00) = 66) and discuss which is the most reliablefigure. £2.50 as within current data. £5 is outside current range so unreliable.State whether time series forecasting could have been used in this situation. No,it is not a time series. If so, why might you choose to use linear regression?Linear regression may be used as the relationship between price and salesappears causal. r and R2 are reasonably high, although the latter indicates thatonly about 71% of change is sales is related to price and therefore other factorsare having quite a large effect.6. A company has a demand history as below: DayDemand12202240323042405260625072308– Calculate forecasts for weeks 5 to 8 using(a) SMA4 (simple moving average)(b) WMA (weighted moving average), with weights 0.4, 0.3, 0.2 and 0.1, with0.4 being the most recent demand value.(c) SES (single exponential smoothing), using 𝛼𝛼 = 0.15 and F4 as 235(d) TAS (trend adjusted exponential smoothing), using 𝛼𝛼 = 0.2, 𝛽𝛽 = 0.3, A3 as230 and T3 as 0.Also, calculate the MAPE (mean absolute percentage error) for each of themethods and say what your result indicates. MAPE’s similar – methodscomparable. DayDemandMA4MAPEWts. 0.4,0.3,0.2,0.1MAPESESalpha=0.15MAPETA alpha = 0.2,beta=0.3TAF=At+TtMAPE1220AtTt2240Use A3=Use T3 =323023004240% erroruse F4 as 235232.000.605260232.5010.6235.009.62235.759.33238.082.24232.6010.546250242.503.0246.001.60239.394.25242.262.82240.323.877230245.006.5249.008.26240.984.77242.071.92245.086.568–245.00MAPE243.00MAPE239.33MAPE243.99MAPE6.76.496.126.99 7. Over a period of three years, a company experiences sales as shown: QuarterYear 1Year 2Year 3130003300350221700210024483900150017684440051005882 a) Calculate an average seasonal index for each quarter.b) If the aggregate demand for year 4 is expected to be 14,800 forecast thesales figures for each quarter of the year.c) Suggest how the forecast might be improved.d) Deseasonalise the data and plot the values along with the original demanddata.e) Looking at your plot, what can you say about the pattern that you see?Upward trend. Could discuss linearity. Could check regression values. Anyregression would need to be done using deseasonalised values. QuarterYear1Year2Year3SI =act/aveQuarterYear1Year2Year3AverageSIForecast130003300350211.21.11.031.114107217002100244820.680.70.720.7259039001500176830.360.50.520.461702444005100588241.761.71.731.736401Average250030003400sum444414800 Deseasonalised=actual/average SIQuarterYear 1Year 2Year 312702.702972.973154.9522428.573000.003497.1431956.523260.873843.4842543.352947.983400.00

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