Assignment -
This assignment should be solved by multiple regression method and regression with the series data (dummy variables).
1. Conducting a study that relates personal savings to personal income (both in billions of $) for the time period from 1935 to 1954. The data is listed chronologically in ex3-pr1.xlsx.
a. Fit a simple regression to the data, using personal income to predict personal saving. Test for the significance of the slope coefficient (at α = 0.05) using the appropriate table. Is it significant? Explain, using information from the Excel output and the appropriate table.
b. What us the equation of this line?
c. Interpret R2. What do you think about its value?
d. Test for serial correlation (at α = 0.05). Explain your results using the information from the Excel output and the appropriate table.
e. Does knowledge of the war years make a significant contribution to the prediction of personal savings? Explain, including a comment on individual coefficients AND the current R2.1
f. Test for serial correlation (at α = 0.05). Again, explain your results using the information from the Excel output and the appropriate table.
2. One of my firms was asked to look into a plan to build a spa very close to the new park that is adjacent to the St. Louis Arch. There was the thought that there has been an upward trend in the number of visitors to the area over the past 14 years. So a variable, "TIME" was included in the initial regression study, to model these 14 years. Likewise, it was believed that the "PRICE" of a gallon of gasoline would also be a good predictor of the number of visitors. So, I would like for you to please check this model for me. Use the data in (ex3-pr2-NEW.xlsx) to examine this relationship. Evaluate all at ... (α = 0.05)
a. Did we get any significant predictors of visitors from this model? (Please explain thoroughly, by discussing the relevant computed t-values and the t from the tables.)
b. What is our BEST regression equation from this model?
c. Is serial correlation a problem in this model? A bit later, some dummy (?) in my office came up with the idea that major celebrations in the area, could also have an effect on the number of visitors. Notably, there were big events in years, 2, 11, & 14. (**Note that the "row-number" in Excel, does not necessarily equal "year".) So perhaps "indicator variables" could be used to model this effect.
d. Please use the information that you learned in "a & b", to model a regression equation that adds this new information. Is this new "celebration idea" significant?
e. So, what about serial correlation with this model? ... (Is it a problem? Is it okay? If it is inconclusive, how could we test it further?)
3. Because of numerous tax breaks that the local government has granted my businesses over the years, they recently ordered that my firms should subsidize the cost of bus service in the St. Louis metro area. As I am looking at the books, I would like to know whether there is a relationship between the annual maintenance cost of a bus and its age, because if there is a relationship, perhaps I can better forecast my costs. Use the data in (ex3-pr3.xlsx) to examine this relationship. (Use α = 0.10 to evaluate these models)
A. Determine the least squares line.
B. Test for the significance of the slope coefficient.
C. Forecast the annual maintenance cost for a five-year-old bus.
It has come to my attention that some of my busses are made by GM and some are made by Ford, and that this could be an additional factor in the determination of my costs. I looked into this and found that busses 5, 9, 10, 12, 13, 16, & 17 are made by GM. (**Note that the "row-number" in Excel, does not necessarily equal "year".)
D. Set up your data, using dummy variables and print the data sheet (Excel Spreadsheet) showing how you set this up...
E. What are the relevant regression equations for Fords and GMs... (continue to use AGE if appropriate)? Do any significant relationships exist?
F. Given your answer on "E", forecast the annual maintenance costs for a five-year-old Ford ... and then ... a five-year-old GM.
(Use α = 0.10 to evaluate this model)
This is easy... I have some quarterly data in ... Ex3-Pr4.xlsx ... which I suspect has some kind of trend and seasonality. (at α = 0.05)
a. First, please set this data up in excel. Save it and show it to me.
b. Is there a significant trend in the data? (Explain, using computed t-values.)
c. Is there significant seasonality in the data? (Explain, using computed t-values.)
d. Please give me the respective forecast equations, for: Quarter 1, Quarter 2, Quarter 3 and Quarter 4.
Attachment:- Assignment File.rar