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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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(ij) = 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(ij) = 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(ij) = 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(ij) = 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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