The stated purpose of the nursing profession is to “deliver excellent care to each patient through the management of resources and to maintain a professional work environment to ensure competence and satisfaction.” In managing nursing services as a CNO, COO, or CEO, how would you measure the performance of your nursing department toward meeting this purpose? List specific dimensions and provide specific examples for the type of healthcare facility that you would like to manage (hospital, clinic, long-term care, home care, or other). Healthcare facility: Hospital

The stated purpose of the nursing profession is to “deliver excellent care to each patient through the management of resources and to maintain a professional work environment to ensure competence and satisfaction.” In managing nursing services as a CNO, COO, or CEO, how would you measure the performance of your nursing department toward meeting this purpose? List specific dimensions and provide specific examples for the type of healthcare facility that you would like to manage (hospital, clinic, long-term care, home care, or other). Healthcare facility: Hospital

All the hospitals are facing increasing demands to forcefully participate … Read More...
Discussion Question – GPS Apps Read Ethics and Issues 2-2 on page 70 of your textbook. If you have a smart phone, have you noticed apps that require location? Should app makers be able to require you to enable tracking or track your activity without your knowledge? Why or why not? What information should they be able to track? Should police be able to track GPS data without warrants? Would you use apps that post your location to social networks? After considering the above questions, write one paragraph for enabling tracking and one against. Your third paragraph: what conclusions have you drawn taking the research and your own experience?

Discussion Question – GPS Apps Read Ethics and Issues 2-2 on page 70 of your textbook. If you have a smart phone, have you noticed apps that require location? Should app makers be able to require you to enable tracking or track your activity without your knowledge? Why or why not? What information should they be able to track? Should police be able to track GPS data without warrants? Would you use apps that post your location to social networks? After considering the above questions, write one paragraph for enabling tracking and one against. Your third paragraph: what conclusions have you drawn taking the research and your own experience?

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MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

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1 CE 321 PRINCIPLES ENVIRONMENTAL ENGINEERING LAB WORKSHEET No. 1 Due: One (1) Week After Each Lab Section, respectively MICROBIOLOGY Environmental engineers employ microbiology in a variety of applications. Testing for coliform bacteria is used to assess whether pathogens may be present in a water or wastewater sample. Coliforms are a type of bacteria that live in the intestines of warm blooded mammals, such as humans and cattle. They are not pathogens, but if they are present in a sample, it is taken as an indication that fecal material from humans or cattle has contacted the water. If fecal material is present, pathogens may be present, too. In water treatment, coliform counts must average less than one colony per 100 milliliters of sample tested. In wastewater treatment, typical acceptable levels might be 200-colonies/100 mL. There are two standard ways to test for coliforms, the Most Probable Number test, MPN (also called the multiple tube fermentation technique, MTF) and the membrane filter test, MF. Several companies market testing systems that are somewhat simpler, but these cannot be used by treatment plants until they receive EPA approval. Two recently accepted methods are the Minimal Media Test (Colilert system), and the Presence-Absence coliform test (P-A test). Wastewater treatment plant operators study the microorganism composition of the activated sludge units in order to assess and predict the performance of the biological floc. A sample of mixed liquor from the aeration basin is examined under the microscope, and based on the relative predominance of a variety of organisms that might be present; the operator can tell if the BOD application rates and wasting rates are as they should be. For your worksheet, please submit the items requested below (10 pts. each): 1. Examine a sample of activated sludge under the microscope (To be done together in class). Use the Atlas, Standard Methods, or other references to identify at least 5 different organisms you observed. List them and sketch them neatly on unlined paper. Describe their motility and any other distinctive characteristics as you observed it. 2. Explain what types of organisms you might expect to find in sludge with a high mean cell residence time (MCRT), and explain why these would predominate over the other types. 3. How can the predominance of a certain kind of microorganism in activated sludge affect the settling characteristics of the sludge? Give several examples. 2 4. Explain why coliforms are used as “indicator organisms” for water and wastewater testing. Name two pathogenic bacteria, two pathogenic viruses, and one pathogenic protozoan sometimes found in water supplies. 5. There is also a test for fecal coliforms. Use your class notes and outside references to explain the distinctions between the tests for total and fecal coliforms. Explain why one would use the fecal coliform test instead of the test for total coliforms. 6. Using outside references, indicate typical coliform limits for surface waters used for swimming and fishing; potable water; and wastewater treatment plant effluent. 7). In the recent past, EPA instituted regulations designed to insure that Giardia are removed from the water. Using your text or other references, explain what kind of organism this is, and explain the way in which EPA has set standards to insure they are removed during water treatment. 8. What is meant by “population dynamics”? What two factors usually control the population dynamics of a mixed culture? 9. Use the MPN test data from the samples prepared for class prior to determine the number of coliforms present in the wastewater samples. Please show your work and explain your reasoning. Total Coliforms Raw Intermediate Effluent Sample Volume No. Positive No. Positive No. Positive 10 5 5 4 1 5 5 2 0.1 5 3 1 0.01 5 1 0 0.001 2 1 —- 0.0001 1 —- —- FecalColiforms Raw Intermediate Effluent Sample Volume No. Positive No. Positive No. Positive 10 5 5 2 1 5 4 0 0.1 5 2 1 0.01 1 0 0 0.001 0 0 —– 0.0001 2 —– —– 3 10. Use the membrane filter test data given in class to determine the number of total coliforms and fecal coliforms present in the sample. Please show your work and explain your reasoning. Total Coliforms Fecal Coliforms Dilution Colonies Dilution Colonies Raw Influent 0.1 mL/100 mL 58 1 mL/100 mL 47 Intermediate 1 mL/100 mL 13 10 mL/100 mL 28 Wetland Effluent 10 mL/100 mL 10 100 mL/100 mL 15

1 CE 321 PRINCIPLES ENVIRONMENTAL ENGINEERING LAB WORKSHEET No. 1 Due: One (1) Week After Each Lab Section, respectively MICROBIOLOGY Environmental engineers employ microbiology in a variety of applications. Testing for coliform bacteria is used to assess whether pathogens may be present in a water or wastewater sample. Coliforms are a type of bacteria that live in the intestines of warm blooded mammals, such as humans and cattle. They are not pathogens, but if they are present in a sample, it is taken as an indication that fecal material from humans or cattle has contacted the water. If fecal material is present, pathogens may be present, too. In water treatment, coliform counts must average less than one colony per 100 milliliters of sample tested. In wastewater treatment, typical acceptable levels might be 200-colonies/100 mL. There are two standard ways to test for coliforms, the Most Probable Number test, MPN (also called the multiple tube fermentation technique, MTF) and the membrane filter test, MF. Several companies market testing systems that are somewhat simpler, but these cannot be used by treatment plants until they receive EPA approval. Two recently accepted methods are the Minimal Media Test (Colilert system), and the Presence-Absence coliform test (P-A test). Wastewater treatment plant operators study the microorganism composition of the activated sludge units in order to assess and predict the performance of the biological floc. A sample of mixed liquor from the aeration basin is examined under the microscope, and based on the relative predominance of a variety of organisms that might be present; the operator can tell if the BOD application rates and wasting rates are as they should be. For your worksheet, please submit the items requested below (10 pts. each): 1. Examine a sample of activated sludge under the microscope (To be done together in class). Use the Atlas, Standard Methods, or other references to identify at least 5 different organisms you observed. List them and sketch them neatly on unlined paper. Describe their motility and any other distinctive characteristics as you observed it. 2. Explain what types of organisms you might expect to find in sludge with a high mean cell residence time (MCRT), and explain why these would predominate over the other types. 3. How can the predominance of a certain kind of microorganism in activated sludge affect the settling characteristics of the sludge? Give several examples. 2 4. Explain why coliforms are used as “indicator organisms” for water and wastewater testing. Name two pathogenic bacteria, two pathogenic viruses, and one pathogenic protozoan sometimes found in water supplies. 5. There is also a test for fecal coliforms. Use your class notes and outside references to explain the distinctions between the tests for total and fecal coliforms. Explain why one would use the fecal coliform test instead of the test for total coliforms. 6. Using outside references, indicate typical coliform limits for surface waters used for swimming and fishing; potable water; and wastewater treatment plant effluent. 7). In the recent past, EPA instituted regulations designed to insure that Giardia are removed from the water. Using your text or other references, explain what kind of organism this is, and explain the way in which EPA has set standards to insure they are removed during water treatment. 8. What is meant by “population dynamics”? What two factors usually control the population dynamics of a mixed culture? 9. Use the MPN test data from the samples prepared for class prior to determine the number of coliforms present in the wastewater samples. Please show your work and explain your reasoning. Total Coliforms Raw Intermediate Effluent Sample Volume No. Positive No. Positive No. Positive 10 5 5 4 1 5 5 2 0.1 5 3 1 0.01 5 1 0 0.001 2 1 —- 0.0001 1 —- —- FecalColiforms Raw Intermediate Effluent Sample Volume No. Positive No. Positive No. Positive 10 5 5 2 1 5 4 0 0.1 5 2 1 0.01 1 0 0 0.001 0 0 —– 0.0001 2 —– —– 3 10. Use the membrane filter test data given in class to determine the number of total coliforms and fecal coliforms present in the sample. Please show your work and explain your reasoning. Total Coliforms Fecal Coliforms Dilution Colonies Dilution Colonies Raw Influent 0.1 mL/100 mL 58 1 mL/100 mL 47 Intermediate 1 mL/100 mL 13 10 mL/100 mL 28 Wetland Effluent 10 mL/100 mL 10 100 mL/100 mL 15

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The heat of fusion of water is 6.01 kJ/mol. The heat capacity of liquid water is 75.3 J/mol · K. The conversion of 50.0 g of ice at 0.00°C to liquid water at 22.0°C requires __________ kJ of heat. A) 3.8×102 B) 21.3 C) 17.2 D) 0.469 E) Insufficient data are given.

The heat of fusion of water is 6.01 kJ/mol. The heat capacity of liquid water is 75.3 J/mol · K. The conversion of 50.0 g of ice at 0.00°C to liquid water at 22.0°C requires __________ kJ of heat. A) 3.8×102 B) 21.3 C) 17.2 D) 0.469 E) Insufficient data are given.

B) 21.3
Name: Lab Time: BIO 218 Experiment Paper Rubric (20 points) General Formatting: (2 pts.) • Margins should be 1 inch top, bottom, left, and right. • Font should be 12 point Times New Roman or similar font. • Double-spaced. • Pages numbered. Title page is unnumbered. Next page is numbered at the bottom right corner with a 2 followed by pages 3, 4, and 5. • All sections must be included: Abstract, Introduction, Methods, Results, Discussion, and Literature Cited. • At least 3 pages (double spaced) but no more than five pages long. • All scientific names should be formatted correctly by italicizing and capitalizing the genus name and having the species name in lowercase (Bufo americanus). • Title page should have a specific title, student name, course, lab section time, and date. Project elements (18 pts. Total) • Abstract (2 points) o Summarize most important points using past tense. Use present tense to suggest a general conclusion which supports or refutes the hypothesis. • Introduction (3 points) o General background on topic and species (state scientific name!) o Discuss the possible tests of the hypothesis. o Reads from general to specific. o States hypothesis/hypotheses to be addressed. May discuss null and all alternative hypotheses. • Methods (2 points) o Reports how experiment was conducted and all materials used. Use enough detail so others could repeat the study. o Discuss the type(s) of data collected. o Discuss how data was to be analyzed/compared/used to test hypothesis. • Results (3 points) o Reports what happened in the experiment. o If comparisons made, discuss how they were made. o Report statistical and other data. Use “significant” only for statistical significance. o NO interpretation of data (no data analysis). o At least one original figure present and formatted correctly. Figures such as pictures and graphs are numbered and have captions underneath. o At least one table present and formatted correctly. Tables such as charts are numbered and have captions above them. • Discussion: (3 points) o Discusses the results of the experiment and ties in how the results fit with the literature. o Use past tense to discuss your results and shift to present tense to discuss previously published information. o States how results supported or refuted the original hypothesis. Hypotheses are never proven! o Ties in results with big picture within topic of biology. • Literature Cited: (2 points: .5 per citation) o At least 2 peer-reviewed journal articles (provided) + 2 peer-reviewed journal articles (found on your own). o References used in text properly. o References all listed in this section are alphabetized by author’s last name and formatted correctly. o All references listed in the Literature Cited section are cited in text. Writing Elements (3 pts.) • Grammar or spelling is error-free and excellent print quality. (1 pt) • Writing is clear and flows logically throughout paper. (1 pt) • Appropriate content in each section? (1 pt) Additional Comments:

Name: Lab Time: BIO 218 Experiment Paper Rubric (20 points) General Formatting: (2 pts.) • Margins should be 1 inch top, bottom, left, and right. • Font should be 12 point Times New Roman or similar font. • Double-spaced. • Pages numbered. Title page is unnumbered. Next page is numbered at the bottom right corner with a 2 followed by pages 3, 4, and 5. • All sections must be included: Abstract, Introduction, Methods, Results, Discussion, and Literature Cited. • At least 3 pages (double spaced) but no more than five pages long. • All scientific names should be formatted correctly by italicizing and capitalizing the genus name and having the species name in lowercase (Bufo americanus). • Title page should have a specific title, student name, course, lab section time, and date. Project elements (18 pts. Total) • Abstract (2 points) o Summarize most important points using past tense. Use present tense to suggest a general conclusion which supports or refutes the hypothesis. • Introduction (3 points) o General background on topic and species (state scientific name!) o Discuss the possible tests of the hypothesis. o Reads from general to specific. o States hypothesis/hypotheses to be addressed. May discuss null and all alternative hypotheses. • Methods (2 points) o Reports how experiment was conducted and all materials used. Use enough detail so others could repeat the study. o Discuss the type(s) of data collected. o Discuss how data was to be analyzed/compared/used to test hypothesis. • Results (3 points) o Reports what happened in the experiment. o If comparisons made, discuss how they were made. o Report statistical and other data. Use “significant” only for statistical significance. o NO interpretation of data (no data analysis). o At least one original figure present and formatted correctly. Figures such as pictures and graphs are numbered and have captions underneath. o At least one table present and formatted correctly. Tables such as charts are numbered and have captions above them. • Discussion: (3 points) o Discusses the results of the experiment and ties in how the results fit with the literature. o Use past tense to discuss your results and shift to present tense to discuss previously published information. o States how results supported or refuted the original hypothesis. Hypotheses are never proven! o Ties in results with big picture within topic of biology. • Literature Cited: (2 points: .5 per citation) o At least 2 peer-reviewed journal articles (provided) + 2 peer-reviewed journal articles (found on your own). o References used in text properly. o References all listed in this section are alphabetized by author’s last name and formatted correctly. o All references listed in the Literature Cited section are cited in text. Writing Elements (3 pts.) • Grammar or spelling is error-free and excellent print quality. (1 pt) • Writing is clear and flows logically throughout paper. (1 pt) • Appropriate content in each section? (1 pt) Additional Comments:

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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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Our readings on statistics this week emphasize the normal distribution and Z-score for determining probabilities in our process and design data, and many of the probabilities we’ll be interested in will be describable in that fashion. The variable control charts that we’ll work on in the next few weeks are based on the validity of the normal distribution as a model for our process data. In this week’s lecture, we discuss three other probability distributions that are used to describe other data samples in this class: hypergeometric, binomial, and Poisson. Each serves a purpose in quality analysis that supplements the more commonly used normal distribution. Think about these three alternate probability distributions in the context of the abridged Red Bead experiment that we performed in our first class of the semester. Describe one or more ways that you might use any of these distributions to explore the experiment, or to explain its results. (Such usage need not be particularly economically valuable to be appropriate in this discussion.) Response Guideline Post your initial response of 1-3 paragraphs (about 150-250 words) early in the week, and then reply to at least two initial responses of your peers, particularly focusing on responses that might differ from your own. Also respond appropriately to anyone who posts questions or comments against your own postings. If you use outside materials to develop your posts, make sure you cite your sources and provide references. Your alternate sources, when used, should be academic or scholarly sources and not web pages or blogs. You don’t need to provide a reference for our text when you use it since we all know that source, but please indicate page numbers when referring to portions of the text. Remember that the initial posting cycle is required of all learners who do not attend the live lecture class (regardless of the class section in which you are enrolled), and is optional for those learners who do attend the live class. The response posting cycle is required for all learners in this class.

Our readings on statistics this week emphasize the normal distribution and Z-score for determining probabilities in our process and design data, and many of the probabilities we’ll be interested in will be describable in that fashion. The variable control charts that we’ll work on in the next few weeks are based on the validity of the normal distribution as a model for our process data. In this week’s lecture, we discuss three other probability distributions that are used to describe other data samples in this class: hypergeometric, binomial, and Poisson. Each serves a purpose in quality analysis that supplements the more commonly used normal distribution. Think about these three alternate probability distributions in the context of the abridged Red Bead experiment that we performed in our first class of the semester. Describe one or more ways that you might use any of these distributions to explore the experiment, or to explain its results. (Such usage need not be particularly economically valuable to be appropriate in this discussion.) Response Guideline Post your initial response of 1-3 paragraphs (about 150-250 words) early in the week, and then reply to at least two initial responses of your peers, particularly focusing on responses that might differ from your own. Also respond appropriately to anyone who posts questions or comments against your own postings. If you use outside materials to develop your posts, make sure you cite your sources and provide references. Your alternate sources, when used, should be academic or scholarly sources and not web pages or blogs. You don’t need to provide a reference for our text when you use it since we all know that source, but please indicate page numbers when referring to portions of the text. Remember that the initial posting cycle is required of all learners who do not attend the live lecture class (regardless of the class section in which you are enrolled), and is optional for those learners who do attend the live class. The response posting cycle is required for all learners in this class.

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Using the Earnings_and_Height dataset, perform the following exercises. 1. Test whether the difference in mean height for men and women is statistically significant? Is it? 2. Does the distribution of height for men and women in the US follow the normal distribution? Answer by looking at detailed summary statistics and high order moments of the data. 3. If you were to select one al observation from the data at random, what is the probability that individual is than sixty seven inches tall? 4a. Run the following regressions and interpret the coefficient on the height variable. I. Regress earnings on height II. Regress log of earning on height III. Regress log earnings on log of height 4b. which model is preferred? 5a. Regress log of earnings on height and height² 5b. is there a non-linear relationship between height and log earnings? 5c. Give a-formula for the effect of a change in height on the change in log earnings. 6. Create the following variables: I. A dummy variable for being-Hispania. ii. A dummy variable for being black. iii. A dummy variable for being female. iv. A set of region dummy variables. 7a. Run the following regression separately by gender: Regress log earnings on height education age black Hispanic 7b. Is there a difference in the estimated effect of height on earnings by gender? 8. Run the following regression: Regress log earnings on height education age black Hispanic female and a set of region indicators, and perform the following tests (and interpret the results): I. Test for the equality of coefficients on the Hispanic and black variables. ii. Test the hypothesis that the coefficients on female, black and Hispanic are all zero. 9a. Run the following regression for men: Regress log earnings on height height² education age black Hispanic and a set of region indicators. Is there evidence of a non-linear relationship between height andlog earnings for men? 9b. Estimate the effect of a one inch increase in height on log earnings for a man starting an average height) 10. Discuss the following threats to internal validity regarding the model in (8): I. measurement error focusing on earnings and height) ii. Omitted variables bias

Using the Earnings_and_Height dataset, perform the following exercises. 1. Test whether the difference in mean height for men and women is statistically significant? Is it? 2. Does the distribution of height for men and women in the US follow the normal distribution? Answer by looking at detailed summary statistics and high order moments of the data. 3. If you were to select one al observation from the data at random, what is the probability that individual is than sixty seven inches tall? 4a. Run the following regressions and interpret the coefficient on the height variable. I. Regress earnings on height II. Regress log of earning on height III. Regress log earnings on log of height 4b. which model is preferred? 5a. Regress log of earnings on height and height² 5b. is there a non-linear relationship between height and log earnings? 5c. Give a-formula for the effect of a change in height on the change in log earnings. 6. Create the following variables: I. A dummy variable for being-Hispania. ii. A dummy variable for being black. iii. A dummy variable for being female. iv. A set of region dummy variables. 7a. Run the following regression separately by gender: Regress log earnings on height education age black Hispanic 7b. Is there a difference in the estimated effect of height on earnings by gender? 8. Run the following regression: Regress log earnings on height education age black Hispanic female and a set of region indicators, and perform the following tests (and interpret the results): I. Test for the equality of coefficients on the Hispanic and black variables. ii. Test the hypothesis that the coefficients on female, black and Hispanic are all zero. 9a. Run the following regression for men: Regress log earnings on height height² education age black Hispanic and a set of region indicators. Is there evidence of a non-linear relationship between height andlog earnings for men? 9b. Estimate the effect of a one inch increase in height on log earnings for a man starting an average height) 10. Discuss the following threats to internal validity regarding the model in (8): I. measurement error focusing on earnings and height) ii. Omitted variables bias

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