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R代写-MATH 7343

时间：2020-12-15

“Final” Homework for MATH 7343

Clearly state your method for analysis and results for each problem. If any computer

printouts are included in your answer, you should label clearly each part of the printout

which problem is it for. Also summarize your conclusion in plain language that non-

statisticians can understand.

1. (40 points)

The file detroit.txt contains data for the number of homicides per 100,000 population

(variable homicide) in the city of Detroit between years 1961 to 1973. (See page 468-469

of the textbook.) The other variables in the data set include police, the number of full-time

police officers per 100,000 population; unemp, the percentage of adults who are employed;

register, the number of handgun registrations per 100,000 per population; and weekly, the

average weekly earnings for city residents. We are interested in effect of these variables on

the homicide rate.

(a) Draw scatter plots of variables homicide vs. each of the four other variables. Are there

any apparent linear relationships from the graphs?

(b) Using homicide as response variable, do four simple linear regressions for each of the

four variables. Which of the four variables, on its own, has statistical significant effect on

the homicide rate? Which of the four variables, on its own, explains the largest percentage

of variation in the homicide rate?

(c) Using the stepwise selection method, finds the best multiple regression model. What

variables are selected? Which of the selected variable, after the other variables effects are

considered, explains the largest percentage of variation in the homicide rate?

(d) Suppose in a particular year, the four variables police, unemp, register and weekly have

the same values as in the year 1970. Construct a 95% prediction interval for the homicide

rate.

(e) Evaluate the fit of the model to data by creating a plot of residuals and a normal

probability plot of the residuals. Discuss your findings.

2. (30 points)

Insurance adjusters from the Shrewd Insurance Company are concerned with the high

estimates they are receiving from Garage Elegance for auto repairs compared to Joe’s

Garage. To verify their suspicions, each of the 15 cars recently involved in an accident was

taken to both garages for separate estimates of repair costs. The data is shown below. (The

repair estimates are in Hundreds of Dollars.) Also can find data in Garage.txt

Car Garage Elegance Joe’s Garage

1 7.6 7.3

2 10.2 9.1

3 9.5 8.4

4 1.3 1.5

5 3.0 2.7

6 6.3 5.8

7 5.3 4.9

8 6.2 5.3

9 2.2 2.0

10 4.8 4.2

11 11.3 11.0

12 12.1 11.0

13 6.9 6.1

14 7.6 6.7

15 8.4 7.5

Find the appropriate statistical method to solve this problem. Report your analysis.

What can you say to the insurance adjusters about your result?

3. (30 points)

Investors use many “indicators” to predict the stock market. Yale Hirsch coded one such

indicator as the “January indicator" in his 1972 book. It states that, if the S&P 500 index is

up in the month of January, then the S&P 500 index will be up for the rest of the year. On

the other hand, if it is down in January, then it will be down for the rest of the year. The

following table gives the data for the 60 years from 1951 to 2010:

Jan.

Feb.-Dec. Up Down

Up 33 11

Down 3 13

(a) State the appropriate null hypothesis and the alternative hypothesis.

(b) I would like to use the 2 -test to solve this problem. However, this is a one-sided

problem while the 2 -test is usually used as a two-sided test. What should I do?

(c) Carry out the test at = 0 05. level.

(d) Explain what your analysis means to the investors.

(e) If you are a portfolio manager, how are you going to use this January indicator?

4. (30 points)

To demonstrate the effect of nematodes (microscopic worms) on plant growth, a botanist

prepares 16 identical planting pots and then introduces different numbers of nematodes

into the pots. A tomato seedling is transplanted into each plot. Here are data on the increase

in height of the seedlings (in centimeters) 16 days after planting.

Nematodes Seedling Growth

0 10.8 9.1 13.5 9.2

1000 11.1 11.1 8.2 11.3

5000 5.4 4.6 7.4 5.0

10000 5.8 5.3 3.2 7.5

(a) I would like to know if the nematodes have any effect on the plant growth at all. Carry

out appropriate statistical analysis. What is your conclusion?

(b) Before conducting the experiment, I decided to test whether the introduction of

nematodes reduces the plant growth. State the appropriate contrast to test this hypothesis,

and carry out the appropriate test.

(c) Looking at the data, it seems that the biggest drop in plant growth is between the group

treated with 1000 nematodes per plant and the group treated with 5000 nematodes per plant.

If I then decide to test whether these two groups do have different plant growth, what is the

appropriate contrast for this test? Carry out the analysis.

5. (40 points).

A study was carried out to see how previous work experience improves the ability of a

programmer to complete a complex programming task. 25 randomly chosen programmers

were asked to complete a complex programming task within a specified time period. For

each programmer, the length of previous programming work experience (in months) was

recorded as well as whether the task was successfully completed (1 indicate success). The

data was presented in the following table (and in programmer.txt).

(a) Does work experience improve the programmer’s ability? Carry out appropriate

statistical analysis. What is your conclusion?

(b) With 95% confidence, give an estimation interval of the improvement in the odds of

completing the task with specified time period for each extra year of work experience.

(Note the data has unit of month.)

(c) The employer values the employee according to the probability of finishing the given

task within the time period. A person with 100% probability of finishing the given task

within the time period is worth the pay of $90,000 per year; A person with 80% probability

of finishing is worth $72,000, etc. Knowing only the work history of an applicant, what

salary (X dollars per year) should the employer pay a programmer with 24 months of

previous work experience? If a second programmer with 18 months of work experience is

willing to accept a yearly salary of $(X-10,000), is the second programmer a better deal for

the company according to the analysis?

Experience in months success

14 0

29 0

6 0

25 1

18 1

4 0

18 0

12 0

22 1

6 0

30 1

11 0

30 1

5 0

20 1

13 0

9 0

32 1

24 0

13 1

19 0

4 0

28 1

22 1

8 1

14 0

6. (20 points) Do 21.5.8 on page 512.

7. For the following data, we wish to test if X has the same mean in group A and group B.

(a) (3 points) Conduct the two sample t-test for this hypothesis.

(b) (7 points) Please conduct a permutation test using the t-test statistic in part (a). Submit

your R code for this permutation test, the R outputs and results of your test. (Hint: while

you can mimic the example R code for the permutation correlation test, please note that the

way of permutation is different. See the lecture notes at end of the non-parametric test

module.)

The data is also in the file PermutationTestData.txt

X Group

1 9.02 A

2 7.88 A

3 10.80 A

4 7.97 A

5 7.81 A

6 8.91 A

7 8.43 A

8 8.88 A

9 8.91 A

10 9.42 A

11 13.16 A

12 9.05 A

13 7.32 B

14 7.95 B

15 7.32 B

16 8.61 B

17 7.01 B

18 7.09 B

19 9.17 B

20 7.78 B

21 7.51 B

22 10.92 B

23 8.09 B

24 7.07 B

25 7.02 B

26 8.46 B

27 9.23 B