Reference no: EM131155919
STATISTICS Homework
1. Load the dataset "PatientSatisfaction.txt" into R. The goal of this analysis is to determine the best subset of predictor variables for determining patient satistfaction.
(a) Indicate which subset of predictor variables are optimal according to the following criteria: AICp, Mallow's Cp, BICp, and PRESSp (i.e. use best subsets variable selection).
(b) Do the four criteria listed above identify the same optimal model? Will this always be the case?
(c) Would forward stepwise regression have any advantages as a screening procedure over best subsets selection?
2. Load the dataset "Bears.csv". Data from n = 19 female wild bears of varying ages are used to estimate the relationship between Y = weight and X = neck circumference.
(a) One of the observations takes on value (x, y) = (10.5, 140). Identify this observation in the dataset. Visually, does this observation appear to be an outlier with respect to any of the following: X, Y, or general the linear relationship between Y and X (i.e. Y |X)? Justify with the appropriate plots.
(b) Compute the leverage for the observation (x, y) = 10.5, 140). What is the cutoff for high leverage in this scenario? Using the rule-of-thumb for leverages presented in class, state whether this point has high leverage?
(c) What is the consequence of including a point with high leverage?
(d) Using the lm() output, calculate each of the following for the (x, y) = (10.5, 140). For some, you will also need the leverage that was calculated above.
i. Studentized residual
ii. Studentized deleted residual
iii. Standardized DFFITS value.
(e) Using the quantities calculated in the previous part should (x, y) = (10.5, 140) be flagged as an outlier?
(f) For the observation (x, y) = (10.5, 140), calculate the following and justify whether this point has strong influence on the model fit?
i. DFBETA
ii. Cook's Distance
3. Data were collected from n = 51 "states" (including the District of Columbia) on the salaries of public school teachers.
(a) Regress Y = average teacher annual salary on X1 = spending per pupil in dollars, X2 a dummy indicator (1/0) for region 2, and X3 = a dummy indicator for region 3. Plot the standardized residuals versus fitted values.
(b) Plot a histogram of the studentized deleted residuals. Are there any outliers in this data? If so, list the index number.
(c) Create a plot of leverages from this model. Are there any outliers with respect to the covariates?
(d) Create plots of Cook's Distances and DFFITS to determine whether any observations have strong influence on the model fit.
Attachment:- HW_Data.zip
|
Examine the political philosophies of each court
: Examine the political philosophies of each court, and indicate significant changes in the law concerning your chosen issue that was witnessed through each court's era. Then, examine the current makeup of the U.S. Supreme Court and modern trends in..
|
|
Discuss the major factors in today society
: Discuss the major factors in today's society that have made the need for independent audits much greater than it was 50 years ago.
|
|
Explain the relationships among audit services
: Explain the relationships among audit services, attestation services, and assurance services, and give examples of each.
|
|
Discuss the reasoning behind this measure of risk
: ome financial theorists consider the variance of the distribution of expected rates of return to be a good measure of uncertainty.- Discuss the reasoning behind this measure of risk and its purpose.
|
|
What is the cutoff for high leverage in the given scenario
: What is the cutoff for high leverage in this scenario? Using the rule-of-thumb for leverages presented in class, state whether this point has high leverage?
|
|
Calculate the work in the compressor and the heat removed
: A stream that contains a mixture of methane (25% by mol) and carbon monoxide is compressed from 1 bar, 35 to 12 bar. The compressor efficiency is 90%. Treating the mixture as an ideal gas, calculate the required work.
|
|
The institute of internal auditors
: The Institute of Internal Auditors (IIA) is an international professional association of more than 170,000 members with global headquarters in Altamonte Springs, Florida. Throughout the world, The IIA is recognized as the internal audit profession's ..
|
|
Identify the internal control deficiencies and recommend
: Superior Co. manufactures automobile parts for sale to the major U.S. automakers. Superior's internal audit staff is to review the internal controls over machinery and equipment and make recommendations for improvements when appropriate. The internal..
|
|
What is the composition of the final mixture
: Compartment A contains 0.2 mol of pure methane at 50 °C, 1 bar. Compartment B contains 0.8 mol of a methane-ethane mixture at 100 °C, 1 bar with ymethane = 0.5. The partition is removed and the system reaches equilibrium.
|