4. Describe “functional aggregation” and discuss how this is relevant to logistics.

4. Describe “functional aggregation” and discuss how this is relevant to logistics.

The inspiration motivating functional aggregation was a rising faith that … Read More...
CIS 343 Homework #1 1. In the game of “craps” two dice are thrown and the outcome of a bet is based on the sum of the two dice. If you bet $1 that the sum is “seven” then you win $4 or lose your dollar. The probability that you win is 6/36=1/6, and P(loss) = 5/6. Find a rough range for a) 200 plays, (b) 20, 000 plays. You must show your work when you compute the SD of the box! [Hint: There are four steps in solving this problem. 1. You must first find the box model, the simplest model has six tickets in the box with some of the tickets +4 and others –1. You must determine how many of each of those two numbers are in the box. 2. Next find the Average of the box and the SD of the box, use “n” not “(n-1)” to compute the SD. 3. Third compute Expected(Winnings)=m•AveOfBox and SD(Winnings)=√m•SDofBox, where m is the number of plays. 4. Finally the Rough Range is Expected(Win)±SD(Win).] 2. Work out the average and SD for the following list: a) 1, 3, 4, 5, 7 Then work out the average and SD for the next list: b) 6, 8, 9, 10, 12 Use n-1 in computing the SD. Are you surprised by the answers? 3. Use “n” in computing SD’s for this problem. a) A list has 10 numbers, each number is a 1, or 2, or 3. If the average is 2 and the SD is 0, find the list. b) A second list has 10 numbers, each number is a 1, or 2, or 3. If the SD is 1, find the list. c) Can the SD be bigger than 1? [This problem is solved by trial and error. Think what center and spread mean! You do not need to use every number for every list. If you do not like the number 3, you may not have to use it] 4. Find the population standard deviation for the following four populations: a) 1, 2, 3, 4, 5 b) 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 [Divide by 5 for the population in a), divide by 10 for the population in b).] c) 2, -1, -1, -1 d) 2, -1, -1, -1, 2, -1, -1, -1 [Divide by 4 for the population in c), divide by 8 for the population in d).]

CIS 343 Homework #1 1. In the game of “craps” two dice are thrown and the outcome of a bet is based on the sum of the two dice. If you bet $1 that the sum is “seven” then you win $4 or lose your dollar. The probability that you win is 6/36=1/6, and P(loss) = 5/6. Find a rough range for a) 200 plays, (b) 20, 000 plays. You must show your work when you compute the SD of the box! [Hint: There are four steps in solving this problem. 1. You must first find the box model, the simplest model has six tickets in the box with some of the tickets +4 and others –1. You must determine how many of each of those two numbers are in the box. 2. Next find the Average of the box and the SD of the box, use “n” not “(n-1)” to compute the SD. 3. Third compute Expected(Winnings)=m•AveOfBox and SD(Winnings)=√m•SDofBox, where m is the number of plays. 4. Finally the Rough Range is Expected(Win)±SD(Win).] 2. Work out the average and SD for the following list: a) 1, 3, 4, 5, 7 Then work out the average and SD for the next list: b) 6, 8, 9, 10, 12 Use n-1 in computing the SD. Are you surprised by the answers? 3. Use “n” in computing SD’s for this problem. a) A list has 10 numbers, each number is a 1, or 2, or 3. If the average is 2 and the SD is 0, find the list. b) A second list has 10 numbers, each number is a 1, or 2, or 3. If the SD is 1, find the list. c) Can the SD be bigger than 1? [This problem is solved by trial and error. Think what center and spread mean! You do not need to use every number for every list. If you do not like the number 3, you may not have to use it] 4. Find the population standard deviation for the following four populations: a) 1, 2, 3, 4, 5 b) 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 [Divide by 5 for the population in a), divide by 10 for the population in b).] c) 2, -1, -1, -1 d) 2, -1, -1, -1, 2, -1, -1, -1 [Divide by 4 for the population in c), divide by 8 for the population in d).]

info@checkyourstudy.com Operations Team Whatsapp( +91 9911743277) CIS 343 Homework #1  1.  … Read More...
Based on the following information, which compound has the strongest intermolecular forces? Substance Hvap (kJ/mol) Argon (Ar) 6.3 Benzene ( 6 6 C H ) 31.0 Ethanol ( 2 5 C H OH) 39.3 Water ( 2 H O ) 40.8 Methane ( 4 CH ) 9.2 A) Argon B) Benzene C) Ethanol D) Water E) Methane

Based on the following information, which compound has the strongest intermolecular forces? Substance Hvap (kJ/mol) Argon (Ar) 6.3 Benzene ( 6 6 C H ) 31.0 Ethanol ( 2 5 C H OH) 39.3 Water ( 2 H O ) 40.8 Methane ( 4 CH ) 9.2 A) Argon B) Benzene C) Ethanol D) Water E) Methane

D) Water
“Sex, Lies and Conversation” Paper For the “Sex, Lies and Conversation” paper you will be writing about the article written by Deborah Tannen that I gave you in class. Your purpose is to evaluate her theory on male and female communication and offer your opinion on whether her theory is valid and still accurate twenty-one years after she published the article. In your introduction, you will identify the author and article (full title at least once) and explain briefly what Tannen’s general theory on male/female communication is to your reader. You’ll also explain that you are evaluating and discussing her theory in order to see if it is still a valid, proven theory. Each body paragraph will focus on one of Tannen’s “differences” between men and women ( the ones we just discussed in class and the one above). For each one you will briefly explain the difference, talk about whether you believe this difference is accurate and true and provide 2-3 examples of people in your life (friend, relative, yourself) who either demonstrates her theory or contradicts it. When you have covered all of her differences, your conclusion will basically move on to discuss whether, based on what you have just said and demonstrated, you believe Tannen’s theory is still current, useful and valid, that it is false or outdated or that it is somewhere in between the two extremes. The paper will run 3 to 4 pages in MLA paper format. Women Men Look at each other when talking Not necessary to look at each other Support/Agree Dismiss Stay on one topic Switch topics frequently Want reactions toward their conversations/feedback Silent/ Listeners They prefer to talk in private areas like home They like to talk in public

“Sex, Lies and Conversation” Paper For the “Sex, Lies and Conversation” paper you will be writing about the article written by Deborah Tannen that I gave you in class. Your purpose is to evaluate her theory on male and female communication and offer your opinion on whether her theory is valid and still accurate twenty-one years after she published the article. In your introduction, you will identify the author and article (full title at least once) and explain briefly what Tannen’s general theory on male/female communication is to your reader. You’ll also explain that you are evaluating and discussing her theory in order to see if it is still a valid, proven theory. Each body paragraph will focus on one of Tannen’s “differences” between men and women ( the ones we just discussed in class and the one above). For each one you will briefly explain the difference, talk about whether you believe this difference is accurate and true and provide 2-3 examples of people in your life (friend, relative, yourself) who either demonstrates her theory or contradicts it. When you have covered all of her differences, your conclusion will basically move on to discuss whether, based on what you have just said and demonstrated, you believe Tannen’s theory is still current, useful and valid, that it is false or outdated or that it is somewhere in between the two extremes. The paper will run 3 to 4 pages in MLA paper format. Women Men Look at each other when talking Not necessary to look at each other Support/Agree Dismiss Stay on one topic Switch topics frequently Want reactions toward their conversations/feedback Silent/ Listeners They prefer to talk in private areas like home They like to talk in public

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Fact Debate Brief Introduction Crime doesn’t pay; it should be punished. Even since childhood, a slap on the hand has prevented possible criminals from ever committing the same offense; whether it was successful or not depended on how much that child wanted that cookie. While a slap on the wrist might or might not be an effective deterrent, the same can be said about the death penalty. Every day, somewhere in the world, a criminal is stopped permanently from committing any future costs, but this is by the means of the death. While effective in stopping one person permanently, it does nothing about the crime world as a whole. While it is necessary to end the career of a criminal, no matter what his or her crime is, we must not end it by taking a life. Through this paper, the death penalty will be proven ineffective at deterring crime by use of other environmental factors. Definition: The death penalty is defined as the universal punishment of death as legally applied by a fair court system. It is important for it to be a fair legal system, as not to confuse it with genocide, mob mentality, or any other ruling without trial. Claim 1: Use of the death penalty is in decline Ground 1: According to the book The Death Penalty: A Worldwide Perspective by Roger Hood and Carolyn Hoyle, published Dec. 8th, 2014, the Oxford professors in criminology say “As in most of the rest of the world, the death penalty in the US is in decline and distributed unevenly in frequency of use” even addressing that, as of April 2014, 18 states no longer have a death penalty, and even Oregon and Washington are considering removing their death penalty laws. Furthermore, in 2013, only 9 of these states still retaining the death penalty actually executed someone. Warrant 1: The death penalty can be reinstated at any time, but so far, it hasn’t been. At the same time, more states consider getting rid of it altogether. Therefore, it becomes clear that even states don’t want to be involved with this process showing that this is a disliked process. Claim 2: Even states with death penalty in effect still have high crime rates. Ground 2: With the reports gathered from fbi.gov, lawstreetmedia.com, a website based around political expertise and research determined the ranking of each state based on violent crime, published September 12th, 2014. Of the top ten most violent states, only three of which had the death penalty instituted (Maryland #9, New Mexico #4, Alaska #3). The other seven still had the system in place, and, despite it, still have a high amount of violent crime. On the opposite end of the spectrum, at the bottom ten most violent states, four of which, including the bottom-most states, do not have the death penalty in place. Warrant 2: With this ranking, it literally proves that the death penalty does not deter crime, or that there is a correlation between having the death penalty and having a decrease in the crime rate. Therefore, the idea of death penalty deterring crime is a null term in the sense that there is no, or a flawed connection. Claim 3: Violent crime is decreasing (but not because if the death penalty) Ground 3 A: According to an article published by The Economist, dated July 23rd, 2013, the rate of violent crime is in fact decreasing, but not because of the death penalty, but rather, because we have more police. From 1995 to 2010, policing has increased one-fifth, and with it, a decline in crime rate. In fact, in cities such as Detroit where policing has been cut, an opposite effect, an increase in crime, has been reported. Ground 3 B: An article from the Wall Street Journal, dated May 28th, 2011, also cites a decline in violent, only this time, citing the reason as a correlation with poverty levels. In 2009, at the start of the housing crisis, crime rates also dropped noticeably. Oddly enough, this article points out the belief that unemployment is often associated with crime; instead, the evidence presented is environmental in nature. Warrant 3: Crime rate isn’t deterred by death penalty, but rather, our surroundings. Seeing as how conditions have improved, so has the state of peace. Therefore, it becomes clear that the death penalty is ineffective at deterring crime because other key factors present more possibility for improvement of society. Claim 4: The death penalty is a historically flawed system. Ground 4A: According to the book The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs by Scott Vollum, published in 2005, addresses how the case of the death penalty emerged to where it is today. While the book is now a decade old, it is used for historical context, particularly, in describing the first execution that took place in 1608. While it is true that most of these executions weren’t as well-grounded as the modern ones that take place now, they still had no effect in deterring crime. Why? Because even after America was established and more sane, the death penalty still had to be used because criminals still had violent behaviors. Ground 4B: According to data from Mother Jones, published May 17th, 2013, the reason why the crime rate was so high in the past could possibly be due to yet another environmental factor (affected by change over time), exposure to lead. Since the removal of lead from paint started over a hundred years ago, there has been a decline in homicide. Why is this important? Lead poisoning in child’s brain, if not lethal, can affect development and lead to mental disability, lower IQ, and lack of reasoning. Warrant 4: By examining history as a whole, there is a greater correlation between other factors that have resulted in a decline in violent crime. The decline in the crime rate has been an ongoing process, but has shown a faster decline due to other environmental factors, rather than the instatement of the death penalty. Claim 5: The world’s violent crime rate is changing, but not due to the death penalty. Ground 5A: According to article published by Amnesty USA in March of 2014, the number of executions under the death penalty reported in 2013 had increased by 15%. However, the rate of violent crime in the world has decreased significantly in the last decade. But, Latvia, for example, has permanently banned the death penalty since 2012. In 2014, the country was viewed overall as safe and low in violent crime rate. Ground 5B: However, while it is true that there is a decline in violent crime rate worldwide, The World Bank, April 17, 2013, reports that the rate of global poverty is decreasing. In a similar vein to the US, because wealth is being distributed better and conditions are improving overall, there is a steady decline in crime rate. Warrant 5: By examining the world as a whole, it becomes clear that it doesn’t matter if the death penalty is in place, violent crime will still exist. However, mirroring the US, as simple conditions improve, so does lifestyle. The death penalty does not deter crime in the world, rather a better quality of life is responsible for that. Works Cited “Death Sentences and Executions 2013.” Amnesty International USA. Amnesty USA, 26 Mar. 2014. Web. 15 Mar. 2015. <http://www.amnestyusa.org/research/reports/death-sentences-and-executions-2013>. D. K. “Why Is Crime Falling?” The Economist. The Economist Newspaper, 23 July 2013. Web. 12 Mar. 2015. <http://www.economist.com/blogs/economist-explains/2013/07/economist-explains-16>. Drum, Kevin. “The US Murder Rate Is on Track to Be Lowest in a Century.”Mother Jones. Mother Jones, 17 May 2013. Web. 13 Mar. 2015. <http://www.motherjones.com/kevin-drum/2013/05/us-murder-rate-track-be-lowest-century>. Hood, Roger, and Carolyn Hoyle. The Death Penalty: A Worldwide Perspective. Oxford: Oxford UP, 2002. 45. Print. Rizzo, Kevin. “Slideshow: America’s Safest and Most Dangerous States 2014.”Law Street Media. Law Street TM, 12 Sept. 2014. Web. 12 Mar. 2015. <http://lawstreetmedia.com/blogs/crime/safest-and-most-dangerous-states-2014/#slideshow>. Vollum, Scott. The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs. Newark, NJ: LexisNexis, 2005. 2. Print. Theis, David. “Remarkable Declines in Global Poverty, But Major Challenges Remain.” The World Bank. The World Bank, 17 Apr. 2013. Web. 15 Mar. 2015. <http://www.worldbank.org/en/news/press-release/2013/04/17/remarkable-declines-in-global-poverty-but-major-challenges-remain>. Wilson, James Q. “Hard Times, Fewer Crimes.” WSJ. The Wall Street Journal, 28 May 2011. Web. 13 Mar. 2015. <http://www.wsj.com/articles/SB10001424052702304066504576345553135009870>.

Fact Debate Brief Introduction Crime doesn’t pay; it should be punished. Even since childhood, a slap on the hand has prevented possible criminals from ever committing the same offense; whether it was successful or not depended on how much that child wanted that cookie. While a slap on the wrist might or might not be an effective deterrent, the same can be said about the death penalty. Every day, somewhere in the world, a criminal is stopped permanently from committing any future costs, but this is by the means of the death. While effective in stopping one person permanently, it does nothing about the crime world as a whole. While it is necessary to end the career of a criminal, no matter what his or her crime is, we must not end it by taking a life. Through this paper, the death penalty will be proven ineffective at deterring crime by use of other environmental factors. Definition: The death penalty is defined as the universal punishment of death as legally applied by a fair court system. It is important for it to be a fair legal system, as not to confuse it with genocide, mob mentality, or any other ruling without trial. Claim 1: Use of the death penalty is in decline Ground 1: According to the book The Death Penalty: A Worldwide Perspective by Roger Hood and Carolyn Hoyle, published Dec. 8th, 2014, the Oxford professors in criminology say “As in most of the rest of the world, the death penalty in the US is in decline and distributed unevenly in frequency of use” even addressing that, as of April 2014, 18 states no longer have a death penalty, and even Oregon and Washington are considering removing their death penalty laws. Furthermore, in 2013, only 9 of these states still retaining the death penalty actually executed someone. Warrant 1: The death penalty can be reinstated at any time, but so far, it hasn’t been. At the same time, more states consider getting rid of it altogether. Therefore, it becomes clear that even states don’t want to be involved with this process showing that this is a disliked process. Claim 2: Even states with death penalty in effect still have high crime rates. Ground 2: With the reports gathered from fbi.gov, lawstreetmedia.com, a website based around political expertise and research determined the ranking of each state based on violent crime, published September 12th, 2014. Of the top ten most violent states, only three of which had the death penalty instituted (Maryland #9, New Mexico #4, Alaska #3). The other seven still had the system in place, and, despite it, still have a high amount of violent crime. On the opposite end of the spectrum, at the bottom ten most violent states, four of which, including the bottom-most states, do not have the death penalty in place. Warrant 2: With this ranking, it literally proves that the death penalty does not deter crime, or that there is a correlation between having the death penalty and having a decrease in the crime rate. Therefore, the idea of death penalty deterring crime is a null term in the sense that there is no, or a flawed connection. Claim 3: Violent crime is decreasing (but not because if the death penalty) Ground 3 A: According to an article published by The Economist, dated July 23rd, 2013, the rate of violent crime is in fact decreasing, but not because of the death penalty, but rather, because we have more police. From 1995 to 2010, policing has increased one-fifth, and with it, a decline in crime rate. In fact, in cities such as Detroit where policing has been cut, an opposite effect, an increase in crime, has been reported. Ground 3 B: An article from the Wall Street Journal, dated May 28th, 2011, also cites a decline in violent, only this time, citing the reason as a correlation with poverty levels. In 2009, at the start of the housing crisis, crime rates also dropped noticeably. Oddly enough, this article points out the belief that unemployment is often associated with crime; instead, the evidence presented is environmental in nature. Warrant 3: Crime rate isn’t deterred by death penalty, but rather, our surroundings. Seeing as how conditions have improved, so has the state of peace. Therefore, it becomes clear that the death penalty is ineffective at deterring crime because other key factors present more possibility for improvement of society. Claim 4: The death penalty is a historically flawed system. Ground 4A: According to the book The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs by Scott Vollum, published in 2005, addresses how the case of the death penalty emerged to where it is today. While the book is now a decade old, it is used for historical context, particularly, in describing the first execution that took place in 1608. While it is true that most of these executions weren’t as well-grounded as the modern ones that take place now, they still had no effect in deterring crime. Why? Because even after America was established and more sane, the death penalty still had to be used because criminals still had violent behaviors. Ground 4B: According to data from Mother Jones, published May 17th, 2013, the reason why the crime rate was so high in the past could possibly be due to yet another environmental factor (affected by change over time), exposure to lead. Since the removal of lead from paint started over a hundred years ago, there has been a decline in homicide. Why is this important? Lead poisoning in child’s brain, if not lethal, can affect development and lead to mental disability, lower IQ, and lack of reasoning. Warrant 4: By examining history as a whole, there is a greater correlation between other factors that have resulted in a decline in violent crime. The decline in the crime rate has been an ongoing process, but has shown a faster decline due to other environmental factors, rather than the instatement of the death penalty. Claim 5: The world’s violent crime rate is changing, but not due to the death penalty. Ground 5A: According to article published by Amnesty USA in March of 2014, the number of executions under the death penalty reported in 2013 had increased by 15%. However, the rate of violent crime in the world has decreased significantly in the last decade. But, Latvia, for example, has permanently banned the death penalty since 2012. In 2014, the country was viewed overall as safe and low in violent crime rate. Ground 5B: However, while it is true that there is a decline in violent crime rate worldwide, The World Bank, April 17, 2013, reports that the rate of global poverty is decreasing. In a similar vein to the US, because wealth is being distributed better and conditions are improving overall, there is a steady decline in crime rate. Warrant 5: By examining the world as a whole, it becomes clear that it doesn’t matter if the death penalty is in place, violent crime will still exist. However, mirroring the US, as simple conditions improve, so does lifestyle. The death penalty does not deter crime in the world, rather a better quality of life is responsible for that. Works Cited “Death Sentences and Executions 2013.” Amnesty International USA. Amnesty USA, 26 Mar. 2014. Web. 15 Mar. 2015. . D. K. “Why Is Crime Falling?” The Economist. The Economist Newspaper, 23 July 2013. Web. 12 Mar. 2015. . Drum, Kevin. “The US Murder Rate Is on Track to Be Lowest in a Century.”Mother Jones. Mother Jones, 17 May 2013. Web. 13 Mar. 2015. . Hood, Roger, and Carolyn Hoyle. The Death Penalty: A Worldwide Perspective. Oxford: Oxford UP, 2002. 45. Print. Rizzo, Kevin. “Slideshow: America’s Safest and Most Dangerous States 2014.”Law Street Media. Law Street TM, 12 Sept. 2014. Web. 12 Mar. 2015. . Vollum, Scott. The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs. Newark, NJ: LexisNexis, 2005. 2. Print. Theis, David. “Remarkable Declines in Global Poverty, But Major Challenges Remain.” The World Bank. The World Bank, 17 Apr. 2013. Web. 15 Mar. 2015. . Wilson, James Q. “Hard Times, Fewer Crimes.” WSJ. The Wall Street Journal, 28 May 2011. Web. 13 Mar. 2015. .

Fact Debate Brief Introduction Crime doesn’t pay; it should be … Read More...
Based on their chemical equations, photosynthesis and cellular respiration have which of the following relationships? Select one: a. equivalent reactions b. incomplete reactions c. opposite reactions Photosynthesis consumes carbon dioxide and releases oxygen, while cellular respiration consumes oxygen and releases carbon dioxide. d. unrelated reactions

Based on their chemical equations, photosynthesis and cellular respiration have which of the following relationships? Select one: a. equivalent reactions b. incomplete reactions c. opposite reactions Photosynthesis consumes carbon dioxide and releases oxygen, while cellular respiration consumes oxygen and releases carbon dioxide. d. unrelated reactions

Info@checkyourstudy.com                                                                                                                                                                                       : opposite reactions
A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a xed-wing aircraft. The vibration of the frame in the vertical direction can be modeled by a spring made of a slender steel bar, such as the one illustrated in Figure 1.23 of the textbook. Here l=0.3 m and m=125 kg. Calculate the cross-sectional area (in cm2) that should be used if the natural frequency is to be fn=800 Hz.

A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a xed-wing aircraft. The vibration of the frame in the vertical direction can be modeled by a spring made of a slender steel bar, such as the one illustrated in Figure 1.23 of the textbook. Here l=0.3 m and m=125 kg. Calculate the cross-sectional area (in cm2) that should be used if the natural frequency is to be fn=800 Hz.

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University of California, Los Angeles Department of Statistics Statistics 100C Instructor: Nicolas Christou Homework 4 Exercise 1 Consider the following simple regression model yi = 0 + 1xi + i, for which E(i) = 0, E(ij) = 0 for i 6= j, and var(i) = 2. The normal equations discussed earlier in class are: n^ 0 + ^ 1 Xn i=1 xi = Xn i=1 yi ^ 0 Xn i=1 xi + ^ 1 Xn i=1 x2i = Xn i=1 xiyi In matrix form this system of two equations with two unknowns can be expressed as follows:  n Pn i=1 P xi n i=1 xi Pn i=1 x2i  ^ 0 ^ 1  =  Pn i=1 P yi n i=1 xiyi  a. Use matrix algebra to nd the solution for the vector ^ = ( ^ 0; ^ 1)0. b. Use matrix algebra to nd the variance covariance matrix of the vector ^ , i.e.  var( ^ 0) cov( ^ 0; 1) cov( ^ 1; 1) var( ^ 1)  : Exercise 2 Consider the following simple regression model for which i  N(0; ). y1 = 0 + 0:5 1 + 1 y2 = 0 ? 1 + 2 y3 = 0 + 0:5 1 + 3 a. Write the above model in matrix form. b. Find the least squares estimates using vectors and matrices. c. Find the variance-covariance matrix of ^ . d. Find the hat matrix. Verify that the sum of the diagonal elements of the hat matrix is equal to 2 ( Pn i=1 hii = k + 1). e. Generate your own data with n = 3 based on this model and verify that the estimates of 0 and 1 are those given by part (b). Exercise 3 Suppose that you need to t the multiple regression model yi = 0 + 1x1i + 2x2i + i, where E(i) = 0, E(ij) = 0 for i 6= j, and var(i) = 2, to the following data: y x1 x2 -43.6 27 34 3.3 33 30 -12.4 27 33 7.6 24 11 11.4 31 16 5.9 40 30 -4.5 15 17 22.7 26 12 -14.4 22 21 -28.3 23 27 It turns out that (X0X)?1 = 0 @ 1:97015 ?0:05623 ?0:01572 ?0:05623 0:00289 ?0:00091 ?0:01572 ?0:00091 0:00174 1 A and X0Y = 0 @ ?52:3 ?1076:3 ?2220:2 1 A a. Find the least squares estimator of = ( 0; 1; 2)0. b. Find the variance-covariance matrix of the previous estimator. c. Compute the estimate s2e of 2. d. Using your answers to parts (b) and (c) nd the variances of ^ 0; ^ 1, and ^ 2. e. Find the tted value ^y1 a nd its variance. f. What is the variance of the rst residual (var(ei))? Exercise 4 Show that the residuals are orthogonal to the matrix X as well as to the tted values ^Y . This is true for simple or multiple regression models. a. e0X = 0. b. e0^Y = 0. c. Use part (a) to show the already known result that Pn i=1 ei = 0.

University of California, Los Angeles Department of Statistics Statistics 100C Instructor: Nicolas Christou Homework 4 Exercise 1 Consider the following simple regression model yi = 0 + 1xi + i, for which E(i) = 0, E(ij) = 0 for i 6= j, and var(i) = 2. The normal equations discussed earlier in class are: n^ 0 + ^ 1 Xn i=1 xi = Xn i=1 yi ^ 0 Xn i=1 xi + ^ 1 Xn i=1 x2i = Xn i=1 xiyi In matrix form this system of two equations with two unknowns can be expressed as follows:  n Pn i=1 P xi n i=1 xi Pn i=1 x2i  ^ 0 ^ 1  =  Pn i=1 P yi n i=1 xiyi  a. Use matrix algebra to nd the solution for the vector ^ = ( ^ 0; ^ 1)0. b. Use matrix algebra to nd the variance covariance matrix of the vector ^ , i.e.  var( ^ 0) cov( ^ 0; 1) cov( ^ 1; 1) var( ^ 1)  : Exercise 2 Consider the following simple regression model for which i  N(0; ). y1 = 0 + 0:5 1 + 1 y2 = 0 ? 1 + 2 y3 = 0 + 0:5 1 + 3 a. Write the above model in matrix form. b. Find the least squares estimates using vectors and matrices. c. Find the variance-covariance matrix of ^ . d. Find the hat matrix. Verify that the sum of the diagonal elements of the hat matrix is equal to 2 ( Pn i=1 hii = k + 1). e. Generate your own data with n = 3 based on this model and verify that the estimates of 0 and 1 are those given by part (b). Exercise 3 Suppose that you need to t the multiple regression model yi = 0 + 1x1i + 2x2i + i, where E(i) = 0, E(ij) = 0 for i 6= j, and var(i) = 2, to the following data: y x1 x2 -43.6 27 34 3.3 33 30 -12.4 27 33 7.6 24 11 11.4 31 16 5.9 40 30 -4.5 15 17 22.7 26 12 -14.4 22 21 -28.3 23 27 It turns out that (X0X)?1 = 0 @ 1:97015 ?0:05623 ?0:01572 ?0:05623 0:00289 ?0:00091 ?0:01572 ?0:00091 0:00174 1 A and X0Y = 0 @ ?52:3 ?1076:3 ?2220:2 1 A a. Find the least squares estimator of = ( 0; 1; 2)0. b. Find the variance-covariance matrix of the previous estimator. c. Compute the estimate s2e of 2. d. Using your answers to parts (b) and (c) nd the variances of ^ 0; ^ 1, and ^ 2. e. Find the tted value ^y1 a nd its variance. f. What is the variance of the rst residual (var(ei))? Exercise 4 Show that the residuals are orthogonal to the matrix X as well as to the tted values ^Y . This is true for simple or multiple regression models. a. e0X = 0. b. e0^Y = 0. c. Use part (a) to show the already known result that Pn i=1 ei = 0.

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I should expect responses to my questions based on these criteria: Question 5 options: 7 days within 12 hours 7 days within 48 hours Sun-Fri within 24 hours Instantly

I should expect responses to my questions based on these criteria: Question 5 options: 7 days within 12 hours 7 days within 48 hours Sun-Fri within 24 hours Instantly

I should expect responses to my questions based on these … Read More...