10-The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour,
and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine
are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour?
32-A power company located in southern Alabama wants to predict the peak power load (i.e., the maximum amount of power that must be generated each day to meet demand) as a function of the daily high temperature (X). A random sample of 25 summer days is chosen, and the peak power load and the high temperature are recorded each day. The file P13_32.xlsx contains these observations.
- Create a scatterplot for these data. Comment on the observed relationship between Y and X.
- Estimate an appropriate regression equation to predict the peak power load for this power |company. Interpret the estimated regression coefficients.
- Analyze the estimated equation’s residuals.
Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.
- Use your final equation to predict the peak power load on a summer day with a high temperature of 100 degrees.
35-The file P13_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars) and the number of units sold (in millions) for eight months.
a. Assume that the only factor influencing monthly sales is advertising. Fit the following two curves to these data: linear (Y 5 a 1 bX) and power (Y 5 aXb). Which equation best fits the data?
b. Interpret the best-fitting equation.
c. Using the best-fitting equation, predict sales during a month in which $60,000 is spent on advertising.
- Problem 10 – Page 696
- Problem 32 – Page 764
- Problem 35 – Page 764
Use of Excel in Forecasting Problems
Excel Analysis Tool Pack
The Excel Analysis Tool Pack is an Excel add-in that is typically included in the Excel screen tool bar after you select the DATA tab. The icon will be titled: “Data Analysis” and is located on the right side of the tool bar. If the tool pack is not appearing, go to the Excel add-ins to add the tool pack to your spreadsheet toolbar. This tool pack contains a number of basic data analysis tools that you may be familiar with; such as: Correlation, Descriptive Statistics, Exponential Smoothing, Histograms, Moving Averages, and so on.
I recommended that you access the tool pack by selecting the “Data Analysis” icon and review the various analysis tools. To get a detailed description of an analtyical tool, select the tool, select Help, and then scroll down the screen to select the function. For instance: Select “Data Analysis” icon à Select “Correlation” à Select “Help” à scroll to the later part of screen to select “Correlation” again à this will provide you with a definition of the function.
Informational video for your review: https://www.youtube.com/watch?v=4lAvbp-yVs8
This informational video will illustrate the use of the Excel data analysis tool for various statistical functions, such as: mean, median, hypothesis, regression analysis. The intent of this video is to ensure that you are aware of additional Excel analysis capabilities, how to access the Tool Pack and what some of the analytical capabilities are.
Hint: There are a number of interactive tutorials online…so, do not hesitate to search the web for additional information. A link for the Lynda tutorial site was provided earlier in the course. However, here is access information if you have not use Lynda as yet: To start using Lynda, go to -> www.esc.edu/lynda (you will need to put this link in your browser). When prompted, log in with your ESC College credentials (email address & password).
Creating Graphics and Including Analysis Results
When working on the two forecasting problems in this Module, it is important that you demonstrate the correct use of Excel analytics by creating: Scattergrams, adding Trendlines, including Regression data / Regression Equation, identifying R-squared value and the use of linear, exponential, power curves for Best Fit analysis, and on so. Finally, graphics should be appropriately labeled (x and y axis). All of these analysis functions can be found in the Excel tool bar after you insert the scattergram plot to your spreadsheet (based on the data that is provided). Once the basic graphic has been created, select the graphic and the tool bar will display the Chart tools: Design, Layout, Format. Select “Layout” to obtain access to the analytical tools required to complete your chart. When asked to interpret data – use your graphic display and analytical results to facilitate the interpretation. For instance: Interpret the estimated regression coefficients? Use the Regression Equation to identify the coefficients and then provide a brief discussion regarding the influence of the coeficients. Be sure it is a “Best Fit” solution. Check your R2 values.
Video – Trend Lines and Regression Analysis in Excel (12 min):
The intent of the following video is to provide you with an overview of adding a trend line to a chart along with the Excel regression analysis. (Note: Video is actually 12 min versus a stated run time of 15 min.)
Again, There are a number of good tutorials online…so, do not hesitate to search the web for additional information. A link for the Lynda tutorial site was provided earlier in the course.