HW2

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California State University, Fullerton *

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361B

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Economics

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Feb 20, 2024

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HW2: PART 1 : FORECASTING I have broken the HW down into two parts for ease of completion. 1. Time is used as an independent variable: a) in all cases of forecasting b) in cases with only an upward trend c) in any case where there are changes through time beyond seasonal differences d) none of the above 2. What is always the first step in forecasting, particularly before deciding which approach to take? a) graphing the data b) assessing trends c) running a forecasting model d) all of the above 3. In my chain of stores, I suspect that my upkeep costs (keeping the store looking clean and trendy to maintain the expectations of my demanding customer base) varies across locations with income (in the 1000s) in the local area and with store square footage (Size). My data are on the Excel spreadsheet that is part of this homework. I am considering buying a competitor’s store and adding it to my chain. I want to forecast my costs if the current owner is spending $6550 for the 2000 square foot location with an average income of 140,000 in the area. 3a) Are the results statistically significant for use? 3b) Is it possible for all independent variables to NOT be significant but for the model as a whole to be statistically significant? 3c) If this happens, how do you determine whether the model is valid? 3d) What do I expect my costs to be based on the information in the question (above)? Give answer to the nearest penny. 3e) What does this answer tell you with regards to the $6550 the previous owner spent? SELECT ALL THAT APPLY. a) the owner was likely underspending to maintain the appearance of the store b) the owner was likely overspending to maintain the appearance of the store c) I didn’t use the previous owner’s spending because my standards may be different than theirs d) none of the above 4. I look at profits (in millions of dollars) in my business for the last 20 years (Excel file). 4a) Is the relationship positive or negative or not significant? 4b) What does this result (from the previous question) mean? i) profits are increasing over time ii) profits are decreasing over time iii) profits are about the same over time iv) I can’t tell 4c) What is my forecasted profit for next year (in millions, same units as dataset), given to 3 decimal places? 4d) What was my predicted profit for year 10 (3 decimal places)? 5. What’s the difference between the regression formula in the last section (regression) and the way it is generally used in forecasting? Instead of being x, the independent variable(s) is/are (select all that apply): i) r ii) t iii) v iv) dummy variables v) none of the above 6. I code the following for my dummy variables. What are some of my errors (select all that apply): Dum1 Dum2 Dum3 1 0 0 0 2 0 0 0 3 1 0 0 0 2 0 i) dummy variables can only be 0 or 1, which they are not in this case (there are 2s and 3s) ii) the coding is wrong as no data point is coded for zeros iii) I cannot finish my dataset with a different number of each season (dummy variable); in other words, Dum1 and Dum2 are coded for twice, while Dum3 is only coded for once iv) all of the above are errors/issues
7. My business sells summer-related adventures, which begin in late spring to early summer (early), the peak summer season (mid), and late summer to early fall (late). I want to forecast my number of customers for next year (all 3 time periods). My data for the last 5 years are in the associated Excel file. Code the seasons and calculate (to 1 decimal place) how many customers are forecast for next year. Note: depending on how you code your seasons, coefficients and other values my differ, but the final forecast should be the same. a) what is the forecast (for number of customers) for next year’s early season (1 decimal place)? b) what is the forecast for next year’s mid season (1 decimal place)? c) what is the forecast for next year’s late season (1 decimal place)? Rerun this again, but this time without trend. d) what is the forecast (for number of customers) for next year’s early season (1 decimal place)? e) what is the forecast for next year’s mid season (1 decimal place)? f) what is the forecast for next year’s late season (1 decimal place)? g) what was the prediction for this last year’s late season (1 decimal place)? Think about how this result compares to the one for the previous question! h) which has the better p-value, with or without trend? HW2: PART 1 - END HW2: PART 2 : FORECASTING 8. The associated Excel file has a dataset on the sheet labelled “Q8” for year (numbered year that has been in business), the season of sales and the profit (in some unit of $). Calculate the forecast for the next year (4 seasons), each with ONE decimal place, no units. 8a) Is this model statistically meaningful (useful)? 8b) What is the forecast for the next winter? 8c) What is the forecast for the next spring? 8d) What is the forecast for the next summer? 8e) What is the forecast for the next fall? 9. Look at the Excel file on the sheet named Q9. Calculate a moving average for k=5. HINT: don’t forget to skip the first cell for the output if you are using the data analysis command! a) what is the value for time 10 (to 1 decimal place)? b) what is the forecast for time 16 (to whole number)? c) which time has the largest forecast error (above or below)? d) what is it (1 decimal place)? e) what is the MSE (2 decimal places)? Now re-run with k=6 including recalculating the MSE. f) what is the forecast for time 16 (to whole number)? g) what is the MSE (2 decimal places)? h) which is better for smoothing this dataset, k=5 or k=6, and why? Now use exponential smoothing on this dataset with alpha (smoothing constant) = 0.4 i) what is the value for time 10 (to 1 decimal place)? j) what is the MSE (2 decimal places)? k) now re-run with alpha=0.3. What is the MSE (2 decimal places)? L) which smoothing constant is better, 0.4 or 0.3 based on MSE? Remember: homework doesn't cover every possible question type or topic. It offers practice for many of the main topics and ideas. HW2: PART 2 - END
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