Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁   
   b₀   
   
   Complete the estimated regression equation (to 2 decimals).
   =   +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
     
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10  
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,   )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,   )

Which Depreciation Method Should We Use?

Atwater Manufacturing Company purchased a new machine especially built to perform one particular function on the assembly line. A difference of opinion has arisen as to the method of depreciation to be used in connection with this machine. Three methods are now being considered:

(a)The straight-line method

(b)The productive-output method

(c)The sum-of-the-years’-digits method

List separately the arguments for and against each of the proposed methods from both the theoretical and practical viewpoints.

Talk-2-Me Corporation produces and markets mobile phones for corporate use. The mobile phones have built in tracking devices and a network enabled shutdown system so that corporate security or the telephone holder can locate and quickly disable a corporation issued cell phone, when necessary.

The cost of producing and installing the shutdown technology is as follow:

Talk-2-Me receives a bid from an outside vendor to produce the shutdown system for the mobile telephones at a cost of $12.00 per cell phone.

Additional Information:

• Power and utilities costs are directly related to producing the shutdown systems.
• Inspection, materials handling, and setup costs are variable costs. However, those costs vary per “production run” rather than per unit. Each production run produces 10 shutdown systems.
• Specialized machine rental costs are fixed costs, however, they are directly associated with producing shutdown systems. Therefore, if the company discontinues producing the shutdown system, they will not incur the related specialized machine rental costs.
• The vendor will produce and deliver the shutdown systems for Talk-2-Me to install.

Required:

1. If Talk-2-Me accepts the vendor’s bid, they will still use the production facility for existing production related activities. At the $12.00-unit cost, should Talk-2-Me accept the vendor’s offer? (Show your work).
2. Assume that if Talk-2-Me accepts the outside vendor’s offer, they could use the new available production capacity to upgrade their cell phone product. Details associated with the upgrade are:
   • Selling price of upgraded phone will increase by $18
   • Power and utilities costs will decrease to $1.25 per unit
   • Additional other variable cost of the upgrade = $14 per unit
   • Additional fixed cost related to the upgrade = $16,000.

Assuming Talk-2-Me will still produce and sell 10,000 units, re-evaluate the vendor’s offer to produce the shutdown system given this new information

The built-in data set treering provides Annual tree-ring widths in normalized units for years from -6000 to 1979. Assume that the n measurements x=(

x₁, x₂,...,x_n

) are a random sample from a population true mean μ and true unknown variance

σ²

. Using R we can define the vector x by the assignment x<-as.vector(treering).
a) Calculate, n, the number of elements in x.  

b)Calculate the sample standard deviation s, of x.  

c) Estimate true mean μ, using this data by calculating the sample mean.  

d) Calculate an unbiased point estimate of the population variance,

σ²

of tree-ring widths.  

e) Assuming normality of tree ring widths, calculate the maximum likelihood estimate of μ?  
f) Calculate the 60th percentile of x using R.  

g) Calculate a

trimmed mean for x using R.  

h) Since the sample size is >30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 96% level and we use a normal critical value, then what critical value should we use?

i) Calculate a 96% confidence interval(using a normal critical value) for μ.
(

,

)

j) How long is the 96% confidence interval just created in part i?  

Baggage Blunders Terminal 5, built by British Airways for $8.6 billion, is Heathrow Airport’s newest state-of-the-art facility. Made of glass, concrete and steel, it is the largest freestanding building in the United Kingdom opened in 2008. With 96 self-service check-in kiosks, more than 90 fast bag drops, 54 standard check-in desks, and over 15 kilometres of suitcase-moving belts that were supposed to be able to process 12,000 bags per hour. Terminal 5 had been planned to ease congestion at Heathrow and improve the flying experience for the 30 million passengers expected to pass though it annually. However, the facility’s design did not initially seem to support those goals. After two decades of planning and 100 million hours of labour, opening day did not work out as planned. Within the first few hours of the terminal’s operation, problems developed. Baggage workers, presumably understaffed, were unable to clear unclaimed luggage fast enough. Many arriving passengers had to endure long delays to get their bags. There were problems for departing passengers as well, as many tried in vain to check in for flights. Planes were allowed to leave with empty cargo holds. At one point on that first day, the airline had no choice but to check in only those passengers with no checked luggage. And it did not help matters when the moving belt system became jammed. Lesser problems also became apparent: a few broken escalators, some hand dryers that did not work, a gate that would not function, and inexperienced ticket sellers who did not know the fares between Heathrow and various stations on the Piccadilly line. By the end of the first day of operation, Britain’s Department of Transportation released a statement calling for British Airways and the airport operator BAA to ‘work hard to resolve these issues and limit disruptions to passengers’. Almost 250 flights in and out of Terminal 5 were cancelled during the first four days of operation because of problems with the baggage-handling system, the temporary suspension of luggage checking and staff lack of knowledge. Some 28,000 bags were delayed, and 9000 items still needed to be returned to their owners by the second week of operation. The airline said the problems were expected to cost it about $16 million. However nine days after the new terminal opened the system was still experiencing problems. BAA’s computer system, which sorts bags before loading onto flights, malfunctioned and baggage had to be sorted manually. British Airways had to cancel 24 flights to and from Terminal 5 as a result of these latest problems. A spokesperson for British Airways described the situation as ‘incredibly disappointing’ and said they were working with BAA to get the problem resolved as quickly as possible. BAA said the problem was entirely its responsibility. (Case taken from M Scott, ‘New Heathrow hub: Slick but no saviour’,Businessweek, 28 March 2008, p.11). Questions: 1) Explain the terms feed-forward, concurrent and feedback control mechanisms. Which of these is of most importance in this situation? Explain your choice. 2) How might immediate corrective action have been used in this situation? How about basic corrective action?

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁
   b₀
   
   Complete the estimated regression equation (to 2 decimals).
   =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )

Daddy Warbucks, a very wealthy investor, built his fortune through his legendary investing knowledge. At present, he has been offered three investments from which he would like to choose one.

The first is a conservative investment that would perform quite well in an expanding economy and only suffer a small loss in a worsening economy. The second is a speculative investment that would perform extremely well in an expanding economy, but do quite poorly in a worsening economy. The last alternative is a countercyclical investment that would suffer some loss in an expanding economy, but perform well in a worsening economy.

Warbucks believes that there are three possible scenarios during the lives of these investments as follows:

· An Expanding Economy

· A Stable Economy

· A Worsening Economy

He is somewhat pessimistic about where the economy is headed, and so has assigned probabilities of 0.1, 0.5, and 0.4 respectively to these three scenarios. He also estimates that his profits under these respective scenarios are shown in the following payoff table.

1. Considering this data, which investment should he make based on an Expected Monetary Value (EMV) criterion?

2. Upon reflection, Daddy Warbucks doesn't have a great deal of confidence in the accuracy of his probability estimates. Which investment should he make under each of the following criteria?

a) Maximax

b) Maximin

c) Realism Criterion with indices of 0.25, 0.65, and 0.85

d) Equally Likely States of Nature e) Minimax Regret

3. Briefly describe how Warbucks might leverage Bayes' Theorem (Bayes' Decision Rule) to improve his confidence about his probability estimates if he believes that the 10% estimate for an expanding economy is accurate, but is unsure about the odds of the other two scenarios.

eBook Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

Program Specifications

The built-in Java Math methods make some calculations much easier. Write a program called "DoTheMath" that accepts as input three floating-point numbers x, y, and z (define them as double) and outputs several calculations:

1. x to the power of y
2. x to the power of (y to the power of z)
3. The absolute value of x
4. The square root of (x*y to the power of z).

Sample Run:

Enter the values for x, y, z:
-3.7 -3 5
 <-- print a blank line before outputting calculations
x to the power y is -0.019742167295125655
x to the power y to the power z is -8.452419664263233E-139
The absolute value of x is 3.7
The square root of x*y to the power z is 410.49459863681534 <-- end with a println

honestly just kind of lost on how to do this.

Consider the natural log transformation (“ln” transformation) of variables labour cost (L_COST), and total number of rooms per hotel (Total_Rooms). 4.1 Use the least squares method to estimate the regression coefficients b0 and b1 for the log-linear model 4.2 State the regression equation 4.3 Give the interpretation of the regression coefficient b1. 4.4 Give an interpretation of the coefficient of determination R2 . Also, test the significance of your model using the F-test. How, does the value of the coefficient of determination affect the outcome of the above test? 4.5 Test whether a 1% increase of the total number of rooms per hotel can increase the labour cost by more than 0.20%? Use the 5% level of significance for this test.

L_COST   Total_Rooms     
2.165.000   412     
2.214.985   313     
1.393.550   265     
2.460.634   204     
1.151.600   172     
801.469   133     
1.072.000   127     
1.608.013   322     
793.009   241     
1.383.854   172     
494.566   121     
437.684   70     
83.000   65     
626.000   93     
37.735   75     
256.658   69     
230.000   66     
200.000   54     
199.000   68     
11.720   57     
59.200   38     
130.000   27     
255.020   47     
3.500   32     
20.906   27     
284.569   48     
107.447   39     
64.702   35     
6.500   23     
156.316   25     
15.950   10     
722.069   18     
6.121   17     
30.000   29     
5.700   21     
50.237   23     
19.670   15     
7.888   8     
3.500   15     
112.181   18     
30.000   10     
3.575   26     
2.074.000   306     
1.312.601   240     
434.237   330     
495.000   139     
1.511.457   353     
1.800.000   324     
2.050.000   276     
623.117   221     
796.026   200     
360.000   117     
538.848   170     
568.536   122     
300.000   57     
249.205   62     
150.000   98     
220.000   75     
50.302   62     
517.729   50     
51.000   27     
75.704   44     
271.724   33     
118.049   25     
40.000   30     
10.000   10     
10.000   18     
70.000   73     
12.000   21     
20.000   22     
36.277   25     
36.277   25     
10.450   31     
14.300   16     
4.296   15     
379.498   16     
1.520   22     
45.000   12     
96.619   34     
270.000   37     
60.000   25     
12.500   10     
1.934.820   270     
3.000.000   261     
1.675.995   219     
903.000   280     
2.429.367   378     
1.143.850   181     
900.000   166     
600.000   119     
2.500.000   174     
1.103.939   124     
363.825   112     
1.538.000   227     
1.370.968   161     
1.339.903   216     
173.481   102     
210.000   96     
441.737   97     
96.000   56     
177.833   72     
252.390   62     
377.182   78     
111.000   74     
238.000   33     
45.000   30     
50.000   39     
40.000   32     
61.766   25     
166.903   41     
116.056   24     
41.000   49     
195.821   43     
96.713   20     
6.500   32     
5.500   14     
4.000   14     
15.000   13     
9.500   13     
48.200   53     
3.000   11     
27.084   16     
30.000   21     
20.000   21     
43.549   46     
10.000   21