forecast 3a

xlsx

School

California State University, Fullerton *

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514

Subject

Industrial Engineering

Date

Jan 9, 2024

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xlsx

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26

Uploaded by SuperHumanSparrowPerson322

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INPUTS Number of Periods of Data Collected = 8 Smoothing Constant (alpha) = 0.3 Smoothing Constant (gamma) = 0.5 MSE = Initial Forecast Value (Level) = 255.0874 MAD = Initial Forecast Value (Trend) = 2.141633 MAPE = LAD = Intercept Slope Period Forecast Forecast Forecast 1 252.9457855948 2 255.0874183295 255.0874 2.141633 3 256.0060223225 256.8621 1.958178 257.2291 4 253.9261956165 257.3521 1.22406 258.8203 5 248.9407335505 255.6855 -0.221252 258.5761 6 245.0485661141 252.3396 -1.783607 255.4643 7 244.1220953996 248.6258 -2.748685 250.556 8 245.867391161 245.8742 -2.750143 245.8771 Perform Desesonalized Values
44.70 5.44 2.19% 10.42 mance measures for Holt's Method
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INPUTS Number of Periods of Data Collected = 8 Number of seasons in a cycle = 3 Outputs Period sales Seasonal index 1 258 252.945785595 102.00% season 1 2 249 254.66666667 0.9777486911 255.08741833 97.61% season 2 3 257 255 1.0078431373 256.006022322 100.39% season 3 4 259 253 1.023715415 253.926195616 5 243 249.33333333 0.9745989305 248.94073355 6 246 246 1 245.048566114 7 249 245 1.0163265306 244.1220954 8 240 245.867391161 Centered Moving Av. Seasonal / Random Desesonalized Values
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MSE = 5.41 MAD = 2.07 MAPE = 0.82% LAD = 3.29 Find the seasonal index for a specific time period Period 9 seasonal index for the period 100.39% step 1: decompose time series template step 2: forecast of each part for week 9 Seasonal index cooresponding to week 9 100.39% Avg deseasonal sales=257.86+(-1.69)*#weeks deseasonal forecast for week 9 242.62339 Step 3: recompose forecasts 243.565408 SUMMARY OUTPUT Regression Statistics Multiple R 0.8599320379946 R Square 0.739483109969547 Adjusted R Square 0.696063628297805 Standard Error 2.65903802222342 Observations 8 ANOVA df SS MS F Regression 1 120.418363 120.418363 17.0311363 Residual 6 42.4228992 7.0704832 Total 7 162.841262 Coefficients Standard Erro t Stat P-value Intercept 257.862662066977 2.07190573 124.456754 1.8145E-11 Period -1.69325245687125 0.41029847 -4.1268797 0.00616851 Performance measures for Classical Decomposition Method - Using regression method for forecasting deseasonalized time series
combine classcial decomposition with holt's method step 1: decompose time series template step 2: forecast of each part for week 9 Seasonal index cooresponding to week 9 100.39% apply holt's method on deseasonal data intercept slope 245.874193 -2.750143 avg deseasonal sales= 245.87+(-2.75)* # week ahead deseasonal forecast for week 9 243.12405 step 3: recompose forecasts 244.068012 Significance F 0.00616851 Lower 95% Upper 95% Lower 95.0%Upper 95.0% 252.792891 262.932433 252.792891 262.932433 -2.6972167 -0.6892883 -2.6972167 -0.6892883
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#VALUE!
INPUTS Number of Periods of Data Collected = 8 Performance measures for forecasted values below MSE = 44.55 MAD = 5.44 MAPE = 0.0219 LAD = 10.46 Absolute Error Absolute Period sales Predicted sales Error Error Squared % Error 1 258 2 249 3 257 258.227777314728 -1.227777 1.227777 1.507437 0.004777 4 259 263.991916790361 -4.991917 4.991917 24.91923 0.019274 5 243 252.405469506847 -9.40547 9.40547 88.46286 0.038706 6 246 256.456142588719 -10.45614 10.45614 109.3309 0.042505 7 249 255.562412692748 -6.562413 6.562413 43.06526 0.026355 8 240 240.009485579315 -0.009486 0.009486 9E-05 3.95E-05
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avg sales= 259.5+(-2.83) *#weeks Intercept 259.5 weeks -2.0833333333 seasonal index 1.01998141378 0.97613595226 257.229051064248 1.00388263397 258.820320865168 1.01998141378 258.576142926716 0.97613595226 255.464268343572 1.00388263397 250.555950570031 1.01998141378 245.87710863865 0.97613595226 1.00388263397 past forecasts based on holt's on deseasonal data
INPUTS Number of Periods of Data Collected = 8 Performance measures for forecasted values below MSE = 22.32 MAD = 4.06 MAPE = 0.0162 LAD = 7.83 Absolute Error Absolute Period sales Predicted sales Error Error Squared % Error 1 258 257.416666666667 0.583333 0.583333 0.340278 0.002261 2 249 255.333333333333 -6.333333 6.333333 40.11111 0.025435 3 257 253.25 3.75 3.75 14.0625 0.014591 4 259 251.166666666667 7.833333 7.833333 61.36111 0.030245 5 243 249.083333333333 -6.083333 6.083333 37.00694 0.025034 6 246 247 -1 1 1 0.004065 7 249 244.916666666667 4.083333 4.083333 16.67361 0.016399 8 240 242.833333333333 -2.833333 2.833333 8.027778 0.011806
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avg sales= 259.5+(-2.83) *#weeks Intercept 259.5 weeks -2.083333
INPUTS Number of Periods of Data Collected = 8 Performance measures for forecasted values below MSE = 8.96 MAD = 2.40 MAPE = 0.0096 LAD = 5.90 Absolute Error Absolute Period sales Predicted sales Error Error Squared % Error 1 258 253.671050129059 4.32895 4.32895 18.73981 0.016779 2 249 254.898206765385 -5.898207 5.898207 34.78884 0.023688 3 257 256.125363401712 0.874637 0.874637 0.764989 0.003403 4 259 257.352520038038 1.64748 1.64748 2.71419 0.006361 5 243 243.761853009102 -0.761853 0.761853 0.58042 0.003135 6 246 248.940429289499 -2.940429 2.940429 8.646124 0.011953 7 249 246.710093737264 2.289906 2.289906 5.243671 0.009196 8 240 239.540483629942 0.459516 0.459516 0.211155 0.001915
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weeks spending sales year week of year 1 750 258 2019 50 2 780 249 2019 51 3 810 257 2019 52 4 840 259 2020 1 5 720 243 2020 2 6 790 246 2020 3 7 785 249 2020 4 8 730 240 2020 5 SUMMARY OUTPUT Regression Statistics Multiple R 0.710730592299 R Square 0.50513797483 50% speaks the x y va Adjusted R Squar0.422660970635 Standard Error 5.455629101111 Observations 8 ANOVA df SS MS F Regression 1 182.2917 182.2917 6.124592 Residual 6 178.5833 29.76389 Total 7 360.875 Coefficients tandard Err t Stat P-value Intercept 259.5 4.250992 61.04458 1.3E-09 weeks -2.08333333333 0.841822 -2.474791 0.048144 SUMMARY OUTPUT Regression Statistics Multiple R 0.895179408247 R Square 0.801346172949 Adjusted R0.721884642129 Standard E3.786534030931 Observatio 8 ANOVA df SS MS F ignificance Regression 2 289.185800163 144.5929 10.08471 0.017589 Residual 5 71.68919983698 14.33784
Total 7 360.875 Coefficients Standard Error t Stat P-value Lower 95% Intercept 181.3183398995 28.78480492923 6.299099 0.001483 107.3246 weeks -1.73640809673 0.597930421331 -2.90403 0.033633 -3.273437 spending 0.098785491102 0.036179127737 2.730455 0.041258 0.005784 RESIDUAL OUTPUT Observation Predicted sales Residuals 1 253.6710501291 4.328949870941 2 254.8982067654 -5.89820676539 3 256.1253634017 0.874636598288 4 257.352520038 1.647479961962 5 243.7618530091 -0.7618530091 6 248.9404292895 -2.9404292895 7 246.7100937373 2.289906262736 8 239.5404836299 0.459516370058
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SUMMARY OUTPUT Regression Statistics Multiple R 0.895179408247 R Square 0.801346172949 Adjusted R Squar 0.721884642129 Standard Error 3.786534030931 Observations 8 ANOVA df Regression 2 Residual 5 Total 7 Coefficients Intercept 181.3183398995 weeks -1.736408096726 spending 0.098785491102 ariables passage of time ignificance F 0.048144 forecast for week 9 240.75 Lower 95%Upper 95% Lower 95.0% Upper 95.0% forecast for week 12 249.0982 269.9018 249.0982 269.9018 234.5 -4.143197 -0.023469 -4.143197 -0.023469 SUMMARY OUTPUT F Regression Statistics Multiple R 0.710731 avg sales= 259.5+(-2.83) *#weeks weeks influences sales x influence Y is long term linear treand there? asking is slope of weeks equal to 0? p-value = 4.8%<5% --> slope is significantly non-zero --> there is a significantly long term linear treand
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R Square 0.505138 Adjusted R 0.422661 Upper 95% Lower 95.0% Upper 95.0% Standard E 5.455629 255.312 107.3246 255.312 Observatio 8 -0.199379 -3.273437 -0.199379 0.191787 0.005784 0.191787 ANOVA df SS MS F Regression 1 182.2917 182.2916666667 6.124591693887 Residual 6 178.5833 29.76388888889 Total 7 360.875 Coefficients tandard Erro t Stat P-value Intercept 259.5 4.250992 61.04457575801 1.29893424E-09 weeks -2.083333 0.841822 -2.47479124249 0.048143982096 RESIDUAL OUTPUT Observation edicted sale Residuals 1 257.4167 0.583333 2 255.3333 -6.333333 3 253.25 3.75 4 251.1667 7.833333 5 249.0833 -6.083333 6 247 -1 7 244.9167 4.083333 8 242.8333 -2.833333
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SS MS F ignificance F 289.185800163 144.5929 10.08471 0.017589 71.68919983698 14.33784 360.875 Standard Error t Stat P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 28.78480492923 6.299099 0.001483 107.3246 255.312 107.3246 255.312 0.597930421331 -2.90403 0.033633 -3.273437 -0.199379 -3.273437 -0.199379 0.036179127737 2.730455 0.041258 0.005784 0.191787 0.005784 0.191787 avg sales= 181.32 + (-1.736) *#weeks
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Significance F 0.048143982096 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 249.098197424 269.9018 249.0982 269.9018 -4.14319718597 -0.023469 -4.143197 -0.023469
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forecast for week 9 264.4762 s + 0.098 * spending
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