Forecasting and Normal Distribution
Part 1: Forecasting
For Part 1, give all answers accurate to two decimal places.
Use data set 1 from the Excel file "Project E Data" for questions #1 to #12.
For #1 to #9, build the indicated forecast model and find the following for each model:
- Forecast for month 24
- MSE
- MAD
1) 4 month moving average
2) 5 month moving average
3) 6 month moving average
4) Weighted average with the following weights
-Most recent month: 50%
-Second most recent month: 25%
-Third most recent month: 25%
5) Weighted average with the following weights
-Most recent month: 45%
-Second most recent month: 19%
-Third most recent month: 18%
-Fourth most recent month: 18%
6) Weighted average with the following weights
-Most recent month: 40%
-Second most recent month: 15%
-Third most recent month: 15%
-Fourth most recent month: 15%
-Fifth most recent month: 15%
7) Exponential smoothing with α = 0.1
8) Exponential smoothing with α = 0.2
9) Exponential smoothing with α = 0.3
10) Considering all the models built in #1 to #9, which one should be used if larger errors are more dangerous than smaller errors?
11) Considering all the models built in #1 to #9, which one should be used if larger errors are not more dangerous than smaller errors?
12) Considering all that you have learned, which model from #1 to #9 would you use? Why? Write at least three sentences to explain your reasoning.
Use Data Set 2 below from the Excel file "Project E Data" for questions #13 to #19.
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Project E Data: Data Set 2
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Quarter
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Revenue
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YEAR 1
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1
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100
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2
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90
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3
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120
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4
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175
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YEAR 2
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1
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115
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2
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105
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3
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150
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4
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190
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YEAR 3
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1
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135
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2
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130
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3
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155
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4
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230
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YEAR 4
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1
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140
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2
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130
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3
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170
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4
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210
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YEAR 5
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1
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200
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2
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140
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3
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195
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4
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260
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For # 13 to 15, build the following models to predict the revenue for quarters 1, 2, 3, and 4 of year 6.
13) Model with random and trend components. Hint: Use simple linear regression from Unit 3.
14) Model with random and seasonal components. The total predicted revenue for Year 5 is 840.
15) Model with random, seasonal, and trend components.
16) Of the three models built for #13 to #15, which one is most appropriate? Hint: Use a multiple regression test.
17) For the model in #14, what quarter had the highest revenue when the seasonal effect was removed?
18) How many other quarters have a higher raw revenue than the quarter from #17?
19) For the model in #14, explain the reason why the four lowest quarters (after the seasonal effect is removed) are all from year 1. What is going on here?
Part 2: Normal Distribution
Be sure to give answer in correct form such as percent or probability and follow the correct rounding rules.
For # 20 to #25, use this data:
The mean income for individuals with a bachelor degree is $60,000 per year with a standard deviation of $16,000 per year.
20) Using Excel, what is the probability of a randomly selected person from this population has an income between $50,000 and $70,000? Use three decimal places.
21) Using Excel, what percent of this population has an income less than $32,000? Round to nearest tenth of percent.
22) Using Excel, from this population, one in how many will have an income over $136,000? Round to nearest whole number.
23) Using the empirical rule and not Excel, what percent of the population will have an income between $44,000 and $76,000?
24) An acquaintance tells you that there is a college program awarding bachelor's degree and these graduates consistently have an income of at least $172,000.
Using specific information from the part of the lesson about z-scores, say if you would believe this person and explain why or why not. Do not use Excel.
25) Consider families where parents and their adult children are in the population, meaning they all have bachelor degrees. Almost always, a parent with income over $100,000 has children with income close to $60,000, and a parent with income under $20,000 has children with income close to $60,000. Why are these situations so common? Use a specific term from the lesson to explain what is going on here.