STAT 3615 Homework 2 Fall 2016 STAT 3615 Homework 2, Fall 2016 Due date: Tuesday, Sept 27, 2016 1. The amygdala and memory (10 points). The amygdala is a brain structure involved in the processing and memory of emotional reactions. In a research project, 10 subjects were shown emotional video clips. They then had their brain scanned with positron emission tomography (PET) and their memory of the clips was assessed quantitatively. Here are the relative amygdala activity and the memory score for each subject: Relative activity Memory score Relative activity Memory score -0.417 31 -0.031 32 -0.258 29 0.120 31 -0.234 29 0.240 35 -0.249 30 0.342 34 -0.156 33 0.654 33 (a) Make a scatterplot that shows the relationship between relative amygdala activity and memory score. (Note: JMP is preferred to be used to make the graph in your homework. You can find the data set on Scholar. It's named \"HW2_1_Amygdala_and_Memory\".) (b) Describe the form of the relationship. Is there a linear pattern? How strong is the relationship? Compute the correlation coefficient. (c) Is the direction of the association positive or negative? Explain in simple language what this suggests about the involvement of the amygdala in the memory of emotional events. 2. A marketing experiment (5 points) compares three different types of packaging for a product (cardboard, wood, and plastic). Each type of packaging can be presented in two different colors (tan and white). Each combination of package type with a particular color is shown to 45 potential customers, who rate the overall attractiveness on a scale of 1 to 8. (a) Identify the factors. (b) How many treatments are possible? List them. (c) Identify the response. 3. Download the file Manatees.jmp from Scholar (30 points). The dataset contains information on the number of powerboats registered in Florida (in thousands) and manatees killed by collisions with powerboats from 1977 to 2012. (a) Identify the explanatory and response variables. (b) Use technology to create an appropriate graph. (c) Based on the graph, describe the form and direction of the relationship. (d) Is it appropriate to calculate the correlation? Explain. If it is appropriate to calculate the correlation, calculate it. 1 STAT 3615 Homework 2 Fall 2016 (e) Find the equation of the least-squares regression line. We expect predictions from this line to be quite accurate, but only if conditions in Florida remain similar to those of the past 36 years. (f) Interpret the slope of the regression line in this context. (g) Calculate and interpret r2 (the coefficient of determination). (h) Since manatees are an endangered species, suppose that Florida will limit the number of powerboat registrations in a given year to 800,000. Predict the number of manatees killed in such a year. Be careful of the fact that the number of registrations in the dataset are recorded in thousands. (i) Suppose the number of powerboat registrations is limited to 200,000 by the state. Explain why you shouldn't use the regression equation you found in part (e) to predict the number of manatees killed. (j) Make the calculation from part (i) anyway and explain why the prediction does not make sense. 4. Grading oysters (10 points). Oysters are categorized for retail as small, medium, or large based on their volume. The grading process is slow and expensive when done by hand. A computer program estimates oyster volume based on the pixel area of 2D images of the oysters. Table 3.3 shows the actual volume (in cm3) and 2D reconstruction (in thousands of pixels) for 30 oysters. (a) Make a scatterplot of the relationship between actual volume (response) and 2D volume reconstruction (explanatory). Find the equation for the corresponding leastsquares regression line. (Note: JMP is required to be used to make the graph in your homework. You can find the data set on Scholar. It's named \"HW2_2_Grading_Oysters\". Use \"Analyze - Fit Y by X\" in JMP. Be careful when choosing X and Y variables.) (b) Use the regression equation to predict the actual volume of an oyster with a 2D reconstruction of 35 thousand pixels. (c) What percent of the variations in actual oyster volume can be explained by the regression model? 2 STAT 3615 Homework 2 Fall 2016 5. Chapter 7 Exercise 7.39 (page 176) Coffee and Depression (10 points) A study examined coffee consumption between 1980 and 2004 for 50,739 American nurses from the Nurses' Health Study who were free of depressive symptoms at baseline in 1996. Ten years later, 2607 nurses had reported a diagnosis of depression and antidepressant use at some point. The study found that depression risk decreased with greater caffeinated coffee consumption (but not for decaf coffee consumption). (a) What type of observational study is this? Explain your answer. (b) The investigators state that \"this study cannot prove that caffeine or caffeinated coffee reduces the risk of depression but only suggests the possibility of such a protective effect\". Explain why this is the case. (c) What would be a possible confounding variable for this study? 6. Chapter 8 Exercises 8.27 (page 202) (10 points). Bird songs have been hypothesized to be a secondary sexual character signaling an individual's health status. Researchers designed an experiment in which they randomly assigned male collared flycatchers (Ficedula albicollis) to two groups. One group received an immune challenge in the form of an injection of sheep red blood cells, and the other group received a placebo injection. The researchers then recorded the changes in song rate (in strophes per minute) after the injection for the 15 males in the immune challenge group and the 12 males in the placebo group. (a) Outline the design of this experiment. (b) Label the birds from 1 through 27. Use software to carry out the randomization your design requires. For (b), use technology, preferably JMP. Assume the birds (male collared flycatchers) are labeled 1 to 27. Using technology, randomly select 12 of the individuals for the placebo injection group. The remaining 15 individuals should be placed in the other group. To receive credit, you will need to list the numbers included in each group (i.e, Group 1 consists of subjects 3,4,7,.... Group 2 consists of 1,2,5,...). 7. Exercise 4.31 (page 115) Predicting tree height (15 points). Measuring tree height is not an easy task. How well does trunk diameter predict tree height? A survey of 958 live trees in an old-growth forest in Canada provides us with the following information: The mean tree height is 15.6 meters (m), with standard deviation 13.4m; the mean diameter, measured at \"breast height\" (1.3 aboveground), is 23.4 centimeters (cm), and the standard deviation is 23.5 cm. The correlation between the height and diameter is very high: r=0.96. (a) What are the slope and intercept of the regression line to predict tree height from trunk diameter? Draw a graph of this regression line. 3 STAT 3615 Homework 2 Fall 2016 (b) The tree diameters ranged from 1 to 101 cm. Predict the height of a tree in this area that is 50 cm in diameter at breast height. Use r2 to assess the reliability of this prediction. NOTE: For part (a), you should do the calculation using the formulas from class. For part (b), you are asked to make a prediction and use r2 to assess the reliability of the prediction. To assess the reliability, just interpret r2. 8 Short Answers (10 points) 8.1 For each of the following graphs, explain why it is inappropriate to calculate the correlation. 8.2 A National Public Radio, Robert Wood Johnson Foundation, Harvard School of Public Health survey was conducted in March 2012 via telephone, interviewing 1508 nationally representative adults aged 18 and over. Of these respondents, 291 had been hospitalized in the past 12 months. The sample in the setting is: (a) all 235 million adults living in the United States. (b) the 1508 people interviewed. (c) the 291 people interviewed who had been hospitalized in the past 12 months. 8.3 The population represented by the survey described in the previous exercise is: (a) all 235 million adults living in the United States. (b) the 1508 people interviewed. (c) the 291 people interviewed who had been hospitalized in the past 12 months. 8.4 In June 2012, SurveyUSA conducted a survey of 665 adults living in California, asking their opinions on the Supreme Court decision on the constitutionality of the Affordable Care Act. 4 STAT 3615 Homework 2 Fall 2016 SurveyUSA broke down the findings for the 330 males and the 335 females in the sample. In the methodology section, we find out that the poll was conducted by telephone and that respondent households were selected at random using random digit dialing (RDD). What type of sample was used for this survey? (a) A simple random sample (SRS) (b) A stratified random sample (c) A multistage random sample Extra Credit (This exercise you might need to look at Figure 8.1 in the textbook, third edition). Try as much as you can, you may receive partial credit for your work. (+10 points) Doctors identify \"chronic tension-type headaches\" as headaches that occur almost daily for at least six months. Can antidepressant medications or stress management training reduce the number and severity of these headaches? Are both together more effective than either alone? (a) Use diagram like Figure 8.1 to display the treatments in a design with two factors: medication, yes or no; and stress management, yes or no. Then outline the design of a completely randomized experiment to compare these treatments. (b) The headache sufferers named below have agreed to participate in the study. Randomly assign the subjects to the treatments. If you use the Simple Random Sample applet or other software, assign all the subjects. Abbott Decker Herrera Lucero Richter Abdalla Devlin Hersch Masters Riley Alawi Engel Hurwitz Morgan Samuels Broden Fuentes Irwin Nelson Smith Chai Garrett Jiang Nho Suarez Chuang Gill Kelley Ortiz Upasani Cordoba Glover Kim Ramdas Wilson Custer Hammond Landers Reed Xiang 5