Consider a 2^8-3 fractional factorial design with design generators F=ABC, G=ABD, and H=BCDE

a)Find the complete defining relation and generate the alias structure using the principle(positive) fraction. Second, determine the design resolution (you need to show your justification).

b)List the basic variables and the design configuration (All 32 design points with the + and – signs. You should show the setting for all 8 factors by using the design generators) (Hint: Here there are 5 basic variables which you can use to generate the entire design)

The questions involve the data set for asking prices of Richmond townhouses obtained on 2014.11.03.
For your subset, the response variable is:
asking price divided by 10000:
askpr=c(65.8, 41.99, 54.8, 44.8, 50.8, 50.5, 54.98, 81.9, 48.5, 51.99, 26.99, 108.8, 57.8, 79.99, 33.7, 55.8, 40.8, 56.88, 46.8, 79.8, 53.8, 45.99, 40.9, 62.9, 48.8, 65.99, 58.39, 57.8, 50.8, 78.8, 68.8, 86.8, 54.8, 68.5, 58.68, 52.4, 51.68, 68.5, 59.8, 57.5, 68.8, 58.8, 53.9, 61.5, 47.9, 47.8, 77.8, 25.9, 60.8, 74.8)
The explanatory variables are:
(i) finished floor area divided by 100
ffarea=c(13.45, 12.9, 11.26, 9.4, 12.27, 12.26, 13.06, 20.95, 14.8, 12.09, 10.5, 23.98, 12.01, 22, 12, 13.06, 12.26, 15.78, 16.2, 15.25, 10.95, 16.01, 16.06, 14, 14.8, 22.78, 15.09, 13.84, 16.6, 19.48, 15.95, 15.08, 15.46, 13.59, 13.96, 16.22, 15.1, 15.76, 17.63, 13.46, 16.9, 17.37, 11.84, 14.5, 12.1, 13.34, 16.5, 6.1, 13.2, 17.48)
(ii) age
age=c(1, 44, 0, 14, 17, 3, 1, 19, 24, 7, 37, 16, 0, 20, 28, 0, 29, 17, 30, 3, 18, 25, 25, 5, 50, 35, 8, 10, 23, 11, 18, 1, 41, 2, 9, 25, 20, 4, 26, 10, 8, 26, 15, 7, 7, 32, 3, 11, 3, 5)
(iii) monthly maintenance fee divided by 10
mfee=c(18.2, 23.2, 24.8, 23.3, 25.2, 18, 19.6, 34.8, 16.1, 18.1, 28, 36.9, 14.2, 26.7, 25.9, 18.6, 19.8, 17.3, 16, 35, 24.7, 33.7, 24.4, 19.6, 25, 57.4, 20.3, 16, 19.9, 20.4, 23.6, 48.8, 31, 17, 22, 36.4, 24.5, 22.1, 32, 22.1, 19.4, 31, 21, 18.7, 18, 24.5, 25.4, 17.1, 18.9, 29.7)
(iv) number of bedrooms
beds=c(3, 3, 2, 2, 2, 3, 3, 1, 3, 3, 2, 3, 3, 3, 2, 3, 3, 4, 4, 2, 2, 3, 2, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 3, 4, 3, 2, 3, 3, 3, 4, 1, 3, 4)
You are to make a prediction of the response variable when ffarea=18, age=11, mfee=27, beds=3.

You are to fit three multiple regression models with the response variable askpr:
(i) 2 explanatory variables ffarea, age
(ii) 3 explanatory variables ffarea, age, mfee
(iii) 4 explanatory variables ffarea, age, mfee, beds
After you have copied the above R vectors into your R session, you can get a dataframe with
richmondtownh=data.frame(cbind(askpr,ffarea,age,mfee,beds))

Please use 3 decimal places for the answers below which are not integer-valued
Part a)
The values of adjusted ?2R2 for the above models with 2, 3 and 4 explanatory variables are respectively:
2 explanatory:
3 explanatory:
4 explanatory:


Part b)
For the best of these 3 models based on adjusted ?2R2, the number of explanatory variables is:


Part c)
For the best of these 3 models based on adjusted ?2R2, the least squares coefficient for ffarea is

and a 95% confidence interval for ???????βffarea is
to

Part d)
For the best of these 3 models based on adjusted ?2R2, get the prediction, SE and 95% prediction interval when the future values of the explanatory variables are: ffarea=18, age=11, mfee=27, beds=3.
prediction:  and its SE  ,
and the upper endpoint of the 95% prediction interval is

4) An association football (soccer) striker never hits the ball above the crossbar. However, in the horizontal direction, his strikes are normally distributed and centered 3 feet to the left of the goal center with a standard deviation of 8 feet. What is the probability that he will score a goal on a given attempt? (Hint: You need to first find the width of a soccer goal. Also, assume that all strikes in the goal region result in a goal.)

1. If n=10, (x-bar)=35, and s=4, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place: __ < μ < __

2. If n=24, (x-bar)=36, and s=6, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.
Give your answers to one decimal place: __ < μ <__

3. If n=19, (x-bar)=32, and s=3, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.
Give your answers to one decimal place: __ < μ <__

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of

1263

chips and a standard deviation of

117 chips

​(a) Determine the30th

percentile for the number of chocolate chips in a bag.

​(b) Determine the number of chocolate chips in a bag that make up the middle

97​%

of bags.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

​

.

SAT scores are normally distributed with a mean of 1200 and a variance of 1600. What is the probability that a random sample of 64 scores will yield a mean score between 1205 and 1210? (what is the probability that a random sample of 16 scores will yield a mean score less than 1192.5?)

An inventor suggested in the nineteenth century that the letter​ "t" made up 6%

of the English language. A random sample of 1400 letters is taken from a randomly​ selected, large​ book, and the​ t's are counted. Complete parts​ (a) through​ (c) below.

a. What value should we expect for our sample percentage of​ t's? We should expect Answer  _____% of the letters in the sample to be​ t's.

​(Type an integer or a decimal. Do not​ round.)

b. Calculate the standard error. SE equals= Answer ________

​(Round to three decimal places as​ needed.)

c. Use your answers to fill in the blanks below. We expect Answer ______ ​t's, give or take Answer ______.

​(Round to one decimal place as​ needed.)

Use the technology​ display, which results from measures of​ self-esteem listed in the table below. The data are from a project to study how levels of​ self-esteem in subjects relate to their perceived​ self-esteem in other target people who were described in writing. The test here works well even though the data are at the ordinal level of measurement. Assume that​ self-esteem measurements are not affected by an interaction between subject​ self-esteem and target​ self-esteem. Is there sufficient evidence to support the claim that the​ self-esteem of the subject​ (low, medium,​ high) has an effect on the measurements of​ self-esteem? Use a

0.050.05

significance level to test the given claim.

LOADING...

Click to view the data table and technology display.

▼

Upper H 0H0.

There

▼

sufficient evidence to warrant rejection of the claim that the​ self-esteem of the subject​ (low, medium,​ high) has an effect on the measurements of​ self-esteem. There

▼

appear to be an effect from an interaction between the​ self-esteem of the subject​ (low, medium,​ high) and the measurements of​ self-esteem.

Click to select your answer(s).

Data Table

a) A country’s sovereign debt is classified according to that country’s capacity to pay its debt as C or high risk (low capacity to pay its debt), B or moderate risk (decent capacity to pay its debt) and A or low risk (high capacity to pay its debt). If for some reason a country is unable to pay its debt then is said to have defaulted. Over the last year out of all the countries that issue debt

• 10% were classified as C

• 30% were classified as B

• The rest were classified as A

• 40% of high risk countries defualted

• 10% of moderate risk countries defualted

• 1% of low risk countries defualted

Given that a country did not defaulted calculate the probability that it was classified as a moderate risk country.

In a recent discussion, you watched this commercial about Abreva. They said that in as little as 2.5 days you can get relief from cold sores In the fine print, it said "Median healing time is 4.1 days 25% of users healed in 2.5 days" Answer the following questions, be sure to number your answer!

1. What shape do you think the data from this study was and why do you think that?

2. Explain why you think the commercial used the median and not the mean

3. What does that 25 represent in the data from the five-number summary?

4. Finally, discuss what, if any, impact this has on when you watch commercials,

An article discusses methods to reduce transportation costs while satisfying demands. In one study, the percent demand that is unmet (y) and the percent of vehicle capacity (x) needed to meet the expected demand were recorded for 15 different scenarios. The results are presented in the following table.

Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.

Compute the least-squares line for predicting unmet demand (y) from vehicle capacity (x). Round the answers to four decimal places.

Predict the unmet demand when the vehicle capacity is 93%. Round the answer to three decimal places.

Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. An article describes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes.

If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? Round the answer to three decimal places.

Predict the frequency for modes with damping ratio 0.75. Round the answer to three decimal places.

Compute the least-squares line for predicting frequency from damping ratio. Round the answers to three decimal places.

Predict the frequency for modes with damping ratio 0.75. Round the answer to three decimal places.

1. Decision trees are often used to select features to be used as inputs to another modeling technique. Discuss how this can be done.

The National Marine Fisheries Services (NMFS) is part of the National Oceanic and Atmospheric Administration (NOAA). NMFS's programs support the conservation and management of living marine resources. In a study by Hays and Marsh reported in the Canadian Journal of Zoology, 71 loggerhead sea turtles were captured and measured off the coast of Britain. The shell lengths of the turtles are shown in the stem-and-leaf plot below.

1|5 5 6 6 6 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9
|
2|0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 2 2 2 3 4 4
2|5 5 5 6 6 7
|
3|0 0 0 3 4 8
|
4|0 5 9
|
5|1 4 5
|
6|0 1 1 4
|
7|5 8
|
8|8 8
|
9|0 0 4 6

1) A loggerhead sea turtle is classified as a juvenile if its shell length is less than 40 centimeters. How many of the turtles in the sample were juveniles?

2) Use the sample to make a point estimate of the mean shell length of all juvenile loggerhead sea turtles that drift from their hatching site (in Florida) to the coast of Britain.

3) Find the standard deviation of the sample of juveniles.

4) Use the sample to make an interval estimate of the mean shell length of juvenile loggerhead sea turtles that drift from their hatching site to the coast of Britain.

a) Use a 90% confidence level

b) Use a 95% confidence level

c) Use a 99% confidence level

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(___,___)

b. If one of the trials is randomly chosen, find the probability that it lasted at least 15 days.

c. If one of the trials is randomly chosen, find the probability that it lasted between 20 and 23 days.

d. 62% of all of these types of trials are completed within how many days? (Please enter a whole number)