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time-series analysis

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The following is a time series data set. Run a time-series analysis for projections of April 2009 in the Healthcare industry of Nashville.

(Run in SPSS and just copy and paste results in microsoft word. Explain your results)

2006-Dec 55010
2006-Nov 55200
2006-Oct 54100
2006-Sep 54050
2006-Aug 54300
2006-Jul 54100
2006-Jun 54070
2006-May 54100
2006-Apr 55200
2006-Mar 57100
2006-Feb 56100
2006-Jan 56200
2002-Jan 55240
2002-Feb 55300
2002-Mar 55500
2002-Apr 55700
2002-May 55700
2002-Jun 55900
2002-Jul 55800
2002-Aug 55900
2002-Sep 56000
2002-Oct 56020
2001-Jan 55400
2001-Feb 55390
2001-Mar 55330
2001-Apr 55280
2001-May 55285
2001-Jun 55276
2001-Jul 55230
2001-Aug 55400
2001-Sep 55440
2001-Oct 55420
2001-Nov 55500
2001-Dec 55600
2000-Jan 55000
2000-Feb 55050
2000-Mar 55020
2000-Apr 55000
2000-May 55020
2000-Jun 55010
2000-Jul 55000
2000-Aug 54080
2000-Sep 54090
2000-Oct 55000
2000-Nov 55000
2000-Dec 55030
1999-Jan 54890
1999-Feb 54900
1999-Mar 54880
1999-Apr 54875
1999-May 54700
1999-Jun 54760
1999-Jul 55770
1999-Aug 55790
1999-Sep 55800
1999-Oct 55800
1999-Nov 55880
1999-Dec 55890
1998-Jan 54200
1998-Feb 54100
1998-Mar 54120
1998-Apr 54175
1998-May 54230
1998-Jun 54300
1998-Jul 54400
1998-Aug 54440
1998-Sep 54550
1998-Oct 54900
1998-Nov 54930
1998-Dec 54900

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Solution Summary

A time-series analysis is achieved.

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See Also This Related BrainMass Solution

Multiple Regression Analysis, Time Series Analysis

See attached data file.

Background:

One day, after reporting the performance of the company to the shareholders, the CEO of A. Fictitious & Co. decided that he would like to quantify the impact of the company's expenditures has on how much sales it generates. In other words, he would like to know if the company increases the amount spent on marketing by one dollar, how large of an increase (or decrease) in sales would be expected? The major categories of expenditures and how much was spent in each are known for the company, as is the total sales generated per quarter for the last five years. He has the data file with the relevant data sent to you, and asks you to do the multiple-regression analysis to find out the answer to his questions. Oh, and he also asks you to do a time-series analysis on the total sales per quarter and forecast the amount of sales expected in the future.

Part I. Multiple Regression:

1. Look over the expenditure categories that the CEO gave you. Check to see if there interaction between the category Capital Equipment and Materials, and the category Salary and Benefits. Namely, do a multiple regression model with quarterly sales as the y-variable and the four expenditure categories given in the Data set as the x-variables. Do a second multiple regression model with four expenditure categories plus an interaction term between the category Capital Equipment and Materials, and the category Salary and Benefits. After comparing the two models, which is the better model? Can you conclude whether the two categories are independent of each other?

2. Based on your analysis in Question 1, write down the best-fit multiple regression equation for this problem with quarterly sales as the y-variable and the expenditure categories as the x-variables; do not forget the interaction term if there is one. Define each variable in the equation.

3. Answer the CEO's question. Namely, for each the four categories of expenditure (marketing, R&D, equipment and supplies, and salaries and benefits), if the CEO increases spending in one category by one million dollars (holding the others fixed), how much increase in sales should he expect? If you found an interaction term, explain its effects as well.

4. Being a very cautious person, you decide to also give the CEO the confidence intervals for the rates of increase your calculated in Question 3. Calculate the 95% confidence intervals for the slopes you calculated in Question 2, including the interaction term if you found one.

5. Being even more cautious - you are reporting the results to the CEO, after all - you decide to do a residual error analysis by applying the F-Test on the entire regression model. Do so, and interpret the results.

Part II. Time-series Analysis

The CEO noticed that he has five years of quarterly sales data in hand, and they form a time series. He decided to also ask you to perform time-series analysis on it, and use it to forecast what future sales are expected to be at the end of 1Q 2009.

6. Plot the quarterly sales as a function of time in your Excel data spreadsheet. From the shape of these graphs, and any analysis that you think is needed, determine what type of trend model is best suitable for this data. Write down the equation for the trend model, and define and explain each of the variables as it applies to this problem.

7. Do a regression analysis on the data for the trend model you decided on in Question 6, and determine the parameters for the model.

8. Answer the CEO's question. Tell him how much sales are expected to be at the end of 1Q 2009. Be careful, and also include the 95% confidence interval for this number.

Part III. Conclusions

9. Write a report to the CEO of your findings. Which expenditure has the largest impact on sales, and which one has the least impact on sales? How fast do you expect sales to increase in time?

10. When tasked to do this analysis, the CEO made a number of assumptions about the data, and what can be extrapolated from it. List down the assumptions he made, and criticize each assumption. Criticize also the conclusions that you drew from your analysis for your report to the CEO. As a starting point, remember that the data covered a period of five years.

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