# Houston Community College System Statistics Worksheet

1.

Consider the following time series data:Month1234567Value23132012182116(a)Choose the correct time series plot.(i)(ii)(iii)(iv)- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv) What type of pattern exists in the data? – Select your answer -Positive trend patternHorizontal patternVertical patternNegative trend pattern(b)Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8.If required, round your answers to two decimal places. Do not round intermediate calculation.MSE: The forecast for month 8: (c)Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8.If required, round your answers to two decimal places. Do not round intermediate calculation.MSE: The forecast for month 8: (d)Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?- Select your answer -3-month moving averageexponential smoothing(e)Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE.Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient. α = 2.Consider the following time series data.QuarterYear 1Year 2Year 31467201433564578(a)Choose the correct time series plot.(i)(ii)(iii)(iv)- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv) What type of pattern exists in the data? – Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonality (b)Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). If the constant is “1” it must be entered in the box. Do not round intermediate calculation.ŷ = + Qtr1 + Qtr2 + Qtr3 (c)Compute the quarterly forecasts for next year based on the model you developed in part (b).If required, round your answers to three decimal places. Do not round intermediate calculation.YearQuarterFt41424344 (d)Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300).ŷ = + Qtr1 + Qtr2 + Qtr3 + t (e)Compute the quarterly forecasts for next year based on the model you developed in part (d).Do not round your interim computations and round your final answer to three decimal places.YearQuarterPeriodFt4113421443154416 (f)Calculate the MSE for the regression models developed in parts (b) and (d). If required, round your intermediate calculations and final answer to three decimal places. Model developed in part (b)Model developed in part (d)MSE Is the model you developed in part (b) or the model you developed in part (d) more effective?The model developed in – Select your answer -part (b)part (d) is more effective because it has the – Select your answer -largersmaller MSE.3.Refer to the gasoline sales time series data in the given table.WeekSales (1,000s of gallons)117221316424517618722820921101911161225(a)Compute four-week and five-week moving averages for the time series.Do not round intermediate calculations. If required, round your answers to two decimal places.WeekSales4-WeekMovingAverage5-WeekMovingAverage117221316424517618722820921101911161225 (b)Compute the MSE for the four-week and five-week moving average forecasts.Do not round intermediate calculations. If required, round your answers to two decimal places.MSE for four-week moving average = MSE for five-week moving average = (c)What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Consider that the MSE for the three-week moving average is 12.852.- Select your answer -ThreeFourFive4.Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.WeekSales (1,000s of gallons)117221316424517618722820921101911161225(a)Show the exponential smoothing forecasts using α = 0.1, and α = 0.2.ExponentialSmoothingWeekα = 0.1α = 0.213(b)Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α = 0.1 or α = 0.2 for the gasoline sales time series?An – Select your answer -α = 0.1α = 0.2 smoothing constant provides the more accurate forecast, with an overall MSE of .(c)Are the results the same if you apply MAE as the measure of accuracy?An – Select your answer -α = 0.1α = 0.2 smoothing constant provides the more accurate forecast, with an overall MAE of .(d)What are the results if MAPE is used?An – Select your answer -α = 0.1α = 0.2smoothing constant provides the more accurate forecast, with an overall MAPE of .5.Consider the following time series:QuarterYear 1Year 2Year 31716862249415135860534788172(a)Choose a time series plot.(i)(ii)(iii)(iv)- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv)What type of pattern exists in the data? Is there an indication of a seasonal pattern? – Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonality(b)Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300).ŷ = + Qtr1 + Qtr2 + Qtr3(c)Compute the quarterly forecasts for next year.YearQuarterFt414243446.Consider the following time series data:Month1234567Value25132111192215(a)Compute MSE using the most recent value as the forecast for the next period.If required, round your answer to one decimal place.What is the forecast for month 8?If required, round your answer to one decimal place. Do not round intermediate calculation.(b)Compute MSE using the average of all the data available as the forecast for the next period.If required, round your answer to one decimal place. Do not round intermediate calculation.What is the forecast for month 8?If required, round your answer to one decimal place.(c)Which method appears to provide the better forecast?- Select your answer -NaïveAll data average 7.The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The table below provides a time series of the cost per unit for the firm’s leading product over the past eight years.Click on the datafile logo to reference the data.YearCost/Unit ($)YearCost/Unit ($)121.20526.80225.90631.00327.10731.90425.90835.20(a)Choose the correct time series plot.(i)(ii) (iii)(iv)- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv) What type of pattern exists in the data? – Select your answer -Positive trend patternNegative trend patternHorizontal pattern (b)Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.If required, round your answers for the parameters to four decimal places and your answer for the MSE to two decimal places. Do not round your intermediate calculations.y-intercept, b0 = Slope, b1 = MSE = (c)What is the average cost increase that the firm has been realizing per year?If required, round your answer to two decimal places.$ (d)Compute an estimate of the cost/unit for next year.If required, round your answer to two decimal places. Do not round your intermediate calculations.$8.Consider the following time series data.Week123456Value191316101914Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.(a)Mean absolute errorIf required, round your answer to one decimal place. (b)Mean squared errorIf required, round your answer to one decimal place. (c)Mean absolute percentage errorIf required, round your intermediate calculations and final answer to two decimal places. (d)What is the forecast for week 7? Year

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3

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5

6

7

8

Cost/Unit ($)

21.20

25.90

27.10

25.90

26.80

31.00

31.90

35.20

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