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Stat S100 Homework 5 Assignment

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Question;1. 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 HEART;1 31;28 24 24;2 30;23 23 29;3 29;24 18 31;4 28;28 23 26;5 27;22 30 26;6 26;25 24 20;7 30;26 24 17;8 28;30 21 19;9 33;22 18 26;10 33;22 22 24;11 22;23 23 26;12 30;25 20 25;13 32;23 23 14;14 29;18 25 11;15 25;27 27 19;16 24;22 14 24;17 27;23 24 20;18 26;22 24 13;19 24;23 25 20;20 31;12 19 18;21 27;23 17 16;22 28;20 18 19;23 21;20 17 23;24 19;22 18 11;25 34;14 22 27;26 24;20 23 18;27 25;17 19 15;28 25;26 19 20;29 20;19 22 18;30 22;23 23 21;31 26;13 22 11;32 29;16 21 14 continued on next page;33 25;17 18 19;34 22;17 15 15;35 24;16 10 18;36 13;20 12 16;a. 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?

 

Paper#61322 | Written in 18-Jul-2015

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