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Autocorrelation and heteroscedasticity

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Open the Cons Trans 59 – 00.xls file. Use the BEA consumption and transfers data to investigate whether heteroscedasticity or autocorrelation is present in the model using the graphical approach (consumption as the dependent variable). Which answer best represents the degree of autocorrelation in the model? Using EXCEL or PHStat2, answer the following:

a) Neither autocorrelation nor heteroscedasticity appear to be present in the model.
b) Autocorrelation appears to be present in the model.
c) Heteroscedasticity appears to be present in the model.
d) Both autocorrelation and heteroscedasticity appear to be present in the model

Refer to the BEA consumption and transfers data from the Cons_Trans_59-00.xls file which was used in Problem 1, above. Analyze the signs of the residuals and values of the residuals to determine which best describes the pattern in the residuals

a) The signs of the residuals are randomly arranged and the values of the residuals remain constant.
b) The signs of the residuals reveal a non-random pattern and the values of the residuals remain constant.
c) The signs of the residuals reveal a non-random pattern and the values of the residuals increase as the transfers increase.
d) The signs reveal are randomly arranged and the values of the residuals increase as the transfers increase.

Use the Cons Trans 59-00.xls file, which was, used in Problems 1 & 2 and PHStat2, Excel, or other means to calculate the d statistic. The calculated d-statistic is:

a) 0.635267892
b) 1.355377418
c) 0.877545537
d) 0.355377418

The dl and du at a 0.01 level of significance in the Durbin-Watson test for autocorrelation are:

a) 1.44 & 1.54, respectively.
b) 1.48 & 1.57, respectively.
c) 1.25 & 1.34, respectively.
d) 1.24 & 1.42, respectively.

Use the results of the Durbin-Watson test in Problems 3 & 4 to determine if autocorrelation exists in the model. Test at the 0.01 level of significance. The statistical conclusion is:

a) No evidence of autocorrelation.
b) No conclusion can be drawn.
c) Autocorrelation exists in the model.
d) Not enough information to determine if autocorrelation exists.

Sandford Tile Case Study: Linear Optimization Problem

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Sandford Tile company makes ceramic and porcelain tile for residentail and commercial use. They produce three different grades of tile for walls, residential flooring, and commercial flooring each of which requires different amounts of materials and production time and generates different contribution to profit. The spreadsheet shows the percentage of materials needed for each grade and the profit per square foot. Each week Sandford tile receives raaw materials shipments and the operations manager must schedule the plan to efficiently use the matierals to maximize profitability. Currently inventory consists of 6000 pounds of clay, 3000 pounds of silica, 5000 pounds of sand, and 8000 pounds of Feldspar. Because demand varies for the different grades marketing estimates that at most 8000 square feet of grade III tile should be produced and that at east 1500 square feet of grade i tiles are required. Each square foot of tile weighs two pounds.
1. Develop a linear optimization model to determine how many of each grade of tile the company should make next week to maximize profit.
2. Implement the model on a spreadsheet and find an optimal solution
3. Explain the sensitivity information for the objective soefficients. What happens in the projit on Grade I is increased by $.05?
4. If an additional 500 pounds of feldspar is available how will the optimal solution be affected?
5. 1,000 pounds of clay are found to be of poor quality, what should the company do?
6. Use the auxilary variable cells technique to handle the bound contraints and generate all shadow prices.

Waiting line statistics question.

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Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers waiting in line behind the person being served?
A. 0.76
B. 0.19
C. 1.33
D. 1.67
E. none of the above

Linear Programming Question by Solver.

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The south fork Feed Company makes a feed mix from four ingredients–oaks, corn, soybean, and vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplements available for the mix. The company has the following requirments for the mix:

-At least 30% of the mix must be soybeans.
-At least 20% of the mix must be the vitamin supplement
-The ratio of corn to oats cannot exceet 2 to 1
-The amount of oats cannot exceed the amount of soybeans
-The mix must be at least 500 pounds

A pound of oats cost $0.50; a pound of corn, $1.20; a pound of soybeans, $060; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the order to minumize cost.
a.Formulate a linear programming model for this problem.
b. Solve the model by using the computer.

Statistics: Predicted Value of Cricket Chirps

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Find the best predicted temperature (in degree F) at a time when a cricket chirps 3000 times in one minute. What is wrong with this predicted value?

Chirps in 1 minute: 882, 1188, 1104, 864, 1200, 1032, 960, 900
Temperature (degree F) 69.7, 93.3, 84.3, 76.3, 88.6, 82.6, 71.6, 79.6

Auto Industry Research Project Examples

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I have to construct a paper with this criteria: as preparation for the final research paper, formulate a theory about the correlation between measurable independent variables (causes) and one measurable dependent variable (the effect). Be sure to have at least two independent variables for proposed research paper.

How do I begin to formulate this? I have an idea about a regression model of the auto industry but how do I determine what the dependent and independent variables are?

Please Provide Answers steps by steps. Thanks!

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The Data of Mail.XLS
Weight Orders
216 6.1
283 9.1
237 7.2
203 7.5
259 6.9
374 11.5
342 10.3
301 9.5
365 9.2
384 10.6
404 12.5
426 12.9
482 14.5
432 13.6
409 12.8
553 16.5
572 17.1
506 15
528 16.2
501 15.8
628 19
677 19.4
602 19.1
630 18
652 20.2

The operations manager of a large mail-order house believes that there is an association between the weight of the mail it receives and the number of orders to be filled. She would like to investigate the relationship in order to predict the number of orders based on the weight of the mail. From an operational perspective, knowledge of the number of orders will help in the planning of the order fulfillment process. A sample of 25 mail shipments is selected within a range of 200 to 700 pounds. The data are in MAIL.xls.

a) Set up a scatter diagram.

b) Assuming a linear relationship, find the regression coefficients, b0, b1, and its regression equation.

c) Interpret the meaning of the slope b1 in this problem.

d) Predict the average number of orders when the weight of the mail is 500 pounds.

e) Determine the coefficient of determination, r2, and interpret its meaning.

f) Find the standard error of the estimate.

g) Evaluate whether the assumptions of regression (LINE) have been seriously violated.

h) How useful do you think this regression model is for predicting predict the number of orders?

i) At the 0.05 level of significance, is there evidence of a linear relationship between the weight of mail and the number of orders received?

j) Set up a 95% confidence interval estimate of the population slope, 1.

k) Set up a 95% confidence interval estimate of the population average number of orders received for a weight of 500 pounds.

l) Set up a 95% confidence interval of the number of orders received for an individual package with a weight of 500 pounds.

m) Explain the difference in the results in k) and l).