stats problems-Homework 5

Question1. Some believe that individuals with a constant sense of time urgency (often called Type-A behavior) are more susceptible to heart disease than the more relaxed individuals. Although most studies of this issue have focused on individuals, some psychologists have investigated geographical areas. They considered the relationship of city-wide heart disease rates and general measures of the pace of life in the city.For each region of the United States (NE, Midwest, South, West) they selected three large metropolitan areas, three medium size cities and three smaller cities. In each city they measured three indicators of pace of life. The variable walk is the walking speed of pedestrians over a distance of 60 feet during business hours on a clear summer day along a main downtown street. Bank is the average time a sample of bank clerks takes to make change for two $20 bills or to give $20 bills for change. The variable talk is obtained by recording responses of postal clerks explaining the difference between regular, certified and insured mail and by dividing the total number of syllables by the time of their response. The researchers also obtained the age-adjusted death rates from ischemic heart disease (a decreased flow of blood to the heart) for each city (heart). The variables have been standardized so there are no units of measurement involved.Row BANK WALK TALK HEART1 31 28 24 242 30 23 23 293 29 24 18 314 28 28 23 265 27 22 30 266 26 25 24 207 30 26 24 178 28 30 21 199 33 22 18 2610 33 22 22 2411 22 23 23 2612 30 25 20 2513 32 23 23 1414 29 18 25 1115 25 27 27 1916 24 22 14 2417 27 23 24 2018 26 22 24 1319 24 23 25 2020 31 12 19 1821 27 23 17 1622 28 20 18 1923 21 20 17 2324 19 22 18 1125 34 14 22 2726 24 20 23 1827 25 17 19 1528 25 26 19 2029 20 19 22 1830 22 23 23 2131 26 13 22 1132 29 16 21 14 continued on next page33 25 17 18 1934 22 17 15 1535 24 16 10 1836 13 20 12 16a. Develop three separate scatterplots with heart as y and bank, walk and talk as x. Interpret the plots.b. Run a regression of bank, walk and talk (x) with heart (y) and analyze the results.c. Drop the least significant variable and rerun the model. Analyze the new output.d. Using only the “best” variable, run another model and interpret your results.e. Run a correlation table for these four variables. Do the correlations support the analyses you have made?f. What are some of the limitations of this study and your conclusions?2. Evolutionary biologists are keenly interested in the characteristics that enable a species to withstand the selective mechanisms of evolution. An interesting variable in this respect is brain size. One might expect that bigger brains are better, but certain penalties seem to be associated with large brains, such as the need for longer pregnancies and fewer offspring. To shed some light on this issue, it is helpful to determine exactly which characteristics are associated with large brains. Data for this problem are in a file on Blackboard.a. Create scatterplots for brain size and each of the independent variables (body, gestation and litter.) Interpret the plot.b. Construct a correlation matrix and interpret the results.c. Regress brain size (y) on the other three variables (x1, x2, x3) and interpret the results.3. You have just been hired by Dubuque, a hot dog manufacturer that produces Dubuque brand hot dogs for the retail market. On your first day at work you receive a disturbing memo indicating that Ball Park, a competing brand, may substantially reduce the price of its hotdog. Dubuque is concerned about the negative impact this might have on its market share.Ball Park produces two kinds of hotdogs. One is regular and the other is a special all-beef hotdog. The current prices are $1.79 and $1.89 per package. Dubuque’s current price is $1.49 and Oscar Mayer’s is $1.55.According to the memo, Ball Park intends to reduce the price of the regular hot dog to $1.45 and the all beef to $1.55.You want to predict Dubuque’s market share under these different scenarios. Some data are available from a scanner study conducted at grocery stores located in the western suburbs of Chicago (on Blackboard). The data are compiled on a weekly level and consist of information on Dubuque’s market share (MKTDUB) along with its price (pdub), as well as Oscar Mayer’s prices (poscar) and Ball Park’s prices (pbpreg) and (pbpbeef). Prices are given in cents and market share is in decimal form.a. To begin the analysis, create scatterplots of all x variables with market share. What do you see as potential relationships?b. Construct a correlations table and interpret the results.c. Run a regression of marketshare on the four price variables and interpret the results.d. Rerun the regression with an improved model and interpret.e. Run a residuals graph. Is there a problem with residuals?f. Going back to the original question, what is the impact on market share by changing the prices of Ball Park from $1.79 for regular and $1.89 for beef to $1.45 and $1.55? Remember that Dubuque’s and Oscar Mayer’s are to remain constant at $1.49 and $1.69.g. What are the effects on market share of lowering the prices (one at a time) for each of the hotdogs?