Statistics Exercise 100C Instructor Assignment
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages
Statistics Exercise 100C Instructor Assignment
Exercise 1 Please refer to homework 5, exercise 4.
a <- read.table(“http://www.stat.ucla.edu/~nchristo/statistics100C/
Consider the multiple regression model: costi = β0 + β1foodi + β2decoti + β3seri + �i, or in matrix form y = Xβ + �, with E(�) = 0 and cov(�) = σ2I. Suppose we want to estimate the vector β = (β0,β1,β2,β3)
subject to the following three constraints:
β0 + 5β1 + 20β2 + β3 = 0
β0 + β1 + β2 + β3 = −25 β0 − 3β1 − β2 + β3 = −40
Answer the following questions:
- Find the constrained least squares estimate of the vector β. The set of the three constraint above can be expressed in matrix form as Cβ − d = 0. Please show all the steps.
- Use R to find the constrained least squares estimate of the vector β. To check your answer, the vector β̂ must satisfy the three constraints.
Exercise 2 An exercise on centering and scaling. Access the data in R as follows:
a <- read.table(“http://www.stat.ucla.edu/~nchristo/statistics_c173_c273/jura.txt”,
These Jura data were collected by the Swiss Federal Institute of Technology at Lausanne. See Goovaerts, P. 1997, “Geostatistics for Natural Resources Evaluation”, Oxford University Press, New-York, 483 p. for more details. Data were recorded at 359 locations scattered in space (see figure below).
The Jura data set
Concentrations of seven heavy metals (cadmium, cobalt, chromium, copper, nickel, lead, and zinc) in the topsoil were measured at each location. The type of land use and rock type was also recorded for each location. The data can be accessed here:
 “x” “y” “Landuse” “Rock” “Cd”
 “Co” “Cr” “Cu” “Ni” “Pb”
The variables x,y are the coordinates. Landuse and Rock represent type of land use (forest, pasture, meadow, tillage) and rock type (Argovian, Kimmeridgian, Sequanina, Portlandian, and Quaternary). The other vari- ables are concerntrations in ppm of the following chemical elements: Cd: Cadmium Co: Cobalt Cr: Chromium Cu: Copper Ni: Nickel Pb: Lead Zn: Zinc
Use Cd as your response variable. Use Co, Cr, Cu, Ni, Pb, Zn as your predictors to answer the following questions.
- Run the multiple regression of Cd on Co, Cr, Cu, Ni, Pb, Zn. Print the R output.
- Center and scale the predictors and run the multiple regression of Cd on the centered and scaled versions of Co, Cr, Cu, Ni, Pb, Zn.
- Compute the variance covariance matrix of β̂ of the model of question (a).
- Using the variance covariance matrix of β̂ find the variance covariance matrix of δ̂ of the model of question (b).
- Compute the correlation matrix of the predictors.
- Compute V IF1 (corresponds to C
- Statistics Exercise 100C Instructor Assignment
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper.
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