INTRO TO PROBABILITY STATISTICS QUESTIONS

Intro to Probability Statistics questions - Mathematics
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Please see the attached file for the questions since what I pasted down here may show incorrectly on the website.1. Consider the following simple linear regression modelyi = β0 +β1xi +εiwith εi independent errors with E [εi] = 0 and Var[εi] = σ2, for i = 1,...,n.ˆ ˆ−σ2∑ni=1xi(a) Show that Cov β0,β1= n∑ni=1 xi2−(∑ni=1 xi)2 .can be expressed as ∑ni=1(xi−x̄)(yi−ȳ).∑ ni = 1 ( x i − x̄ ) 2(b) Show that the OLS βˆ12. Consider the file “reading.csv” included with this homework assignment as an attachment. The file contains average reading scores of third-graders from several elementary schools on a standardized test in each of two suc- cessive years (1982 and 1983).(a) Plot the reading scores in 1983 (this is your outcome or response vari- able) versus the scores in 1982 (this is your covariate or predictor). Does the relationship appear linear? You can use the read.table orread.csv commands in R to read in the data.(b) Use the following summary statistics to calculate (by hand) the OLSof β0 and β1(c) State the assumption of simple linearthese assumptions are satisfied when fitting a linear regression model to this dataset. Provide the necessary evidence that the assumptions are/are not satisfied.(d) John took the exam in 1982 but not the exam in 1983. His score in 1982 was 250. Predict his score in 1983 according to the simple linear regression model. If it turns out John took the exam in 1983 and his score was 320, what is the error of the predicted value?(e) Confirm your results in (b) by fitting the linear regression in R. stats120c_hwk8_sp2020.pdf Unformatted Attachment Preview STATS 120C: Introduction to Probability and Statistics III Homework # 8 due Friday May 29, 2020 at 5:00PM General instructions: Please write by hand, on top of the first page of the homework the following statement (shown below in blue, in italics): In submitting this homework, I pledge on my honor that I have behaved ethically, according to the rules of the Office of Academic Affairs and Student Contact. [Add this if you have collaborated on the homework with other classmates] I have collaborated with XXX, YYY and ZZZ [Include the names of all the students with whom you have collaborated] [Signature and date] If you have problems including this statement, please contact me to explain your reasons not to include the statement. Students whose homework don’t include the statement will be contacted to discuss why the statement is missing. Please show your work. Failure to show work, will result in failure to obtain full credits even for correct answers. If using R to answer questions, please include all code and output in your problem solution. 1. Consider the following simple linear regression model yi = β0 + β1 xi + εi with εi independent errors with E [εi ] = 0 and Var [εi ] = σ2 , for i = 1, . . . , n.   −σ2 n x (a) Show that Cov βˆ 0 , βˆ 1 = n 2 ∑i=1n i 2 . n ∑i=1 xi −(∑i=1 xi ) (b) Show that the OLS βˆ 1 can be expressed as ∑ni=1 (xi −x̄)(yi −ȳ) . 2 ∑ni=1 (xi −x̄) 2. Consider the file “reading.csv” included with this homework assignment as an attachment. The file contains average reading scores of third-graders from several elementary schools on a standardized test in each of two successive years (1982 and 1983). (a) Plot the reading scores in 1983 (this is your outcome or response variable) versus the scores in 1982 (this is your covariate or predictor). Does the relationship appear linear? You can use the read.table or read.csv commands in R to read in the data. (b) Use the following summary statistics of β0 and β1 ∑40 i=1 xi = 2 = (x − ∑40 i=1 i x̄) ∑40 i=1 xi yi = ∑40 i=1 yi = to calculate (by hand) the OLS 10, 800 57, 690 3, 002, 696 10, 950 (c) State the assumption of simple linear regression and check whether these assumptions are satisfied when fitting a linear regression model to this dataset. Provide the necessary evidence that the assumptions are/are not satisfied. (d) John took the exam in 1982 but not the exam in 1983. His score in 1982 was 250. Predict his score in 1983 according to the simple linear regression model. If it turns out John took the exam in 1983 and his score was 320, what is the error of the predicted value? (e) Confirm your results in (b) by fitting the linear regression in R. ... Purchase answer to see full attachment
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Throughout your nurse practitioner program Vignette Understanding Gender Fluidity Providing Inclusive Quality Care Affirming Clinical Encounters Conclusion References Nurse Practitioner Knowledge Mechanics and word limit is unit as a guide only. The assessment may be re-attempted on two further occasions (maximum three attempts in total). All assessments must be resubmitted 3 days within receiving your unsatisfactory grade. You must clearly indicate “Re-su Trigonometry Article writing Other 5. June 29 After the components sending to the manufacturing house 1. In 1972 the Furman v. Georgia case resulted in a decision that would put action into motion. Furman was originally sentenced to death because of a murder he committed in Georgia but the court debated whether or not this was a violation of his 8th amend One of the first conflicts that would need to be investigated would be whether the human service professional followed the responsibility to client ethical standard.  While developing a relationship with client it is important to clarify that if danger or Ethical behavior is a critical topic in the workplace because the impact of it can make or break a business No matter which type of health care organization With a direct sale During the pandemic Computers are being used to monitor the spread of outbreaks in different areas of the world and with this record 3. Furman v. Georgia is a U.S Supreme Court case that resolves around the Eighth Amendments ban on cruel and unsual punishment in death penalty cases. The Furman v. Georgia case was based on Furman being convicted of murder in Georgia. 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