Written Assignment Two Report Guidelines: o Must be organized neatly and typed. You may use Microsoft word to type the assignment. o Clearly indicate the assignment number on papers. o Electronic copies of you work should be submitted on-line. o You need to hand in individual work. You may talk with each other about the problems; however, I do not want to see word-for-word assignments. Everything in the assignment must be your own work. You are not allowed to use classmate's Minitab Express output. Using Minitab Express output that is not your own is a violation of academic integrity. o No late assignments will be accepted. Please review the Minitab Express Tutorial on Correlation and Regression. All bold and underlined statements correspond with Minitab Express output. Data can be found at on NUoodle - Minitab Express File Assignment Two 1. Changing Units - How does it affect correlation and the LSR Line? How does the fuel consumption of a car change as its speed increases? Here are data from the Federal Highway Administration report for fuel efficiency of vehicles. Source: West, B.H., R.N. McGill, J.W. Hodgson, S.S. Sluder, and D.E. Smith, Development and Verification of Light-Duty Model Emissions and Fuel Consumption Values for Traffic Models , FHWA Report (in press), Washington, DC, April 1997, and additional project data, April 1998. (Additional resources: www.fhwa-tsis.com) Speed (mph) 15 20 25 30 35 40 45 50 55 60 65 70 75 MPG 24.4 27.9 30.5 31.7 31.2 31.0 31.6 32.4 32.4 31.4 29.2 26.8 24.8 In the Minitab Express worksheet, the speed (mph) and the fuel (mpg) are recorded in C1 and C2 respectively. Using the following conversions 1 mph = 1.609344 kilometers / hr 1 mile per gallon = 0.425143707 kilometers / L the speed has been converted to kilometer per hour (km/h) in C4 and fuel consumption has been converted to kilometer per liter (km/L) in C5. a. Determine the explanatory and response variable. b. Use Minitab Express to calculate a simple linear regression line of speed (mph) and the fuel (US gallon/mile) used. Include the regression equation and fitted line plot scatterplot in the document you submit. (Use columns C1 and C2. Make sure the explanatory variable (speed) is on the horizontal axis.) c. Use Minitab Express to make to calculate a simple linear regression line of speed (km/hr) and the fuel (liters/100km) used. (Use columns C4 and C5. Include the regression equation and fitted line plot scatterplot in the document you submit. Make sure the explanatory variable (speed) is on the horizontal axis.) d. Are there any differences in the plots in b and c? e. Use Minitab Express to compute correlation for the both sets of data (columns C1 and C2 together and columns C4 and C5 together) Did correlation change when the units were changed? f. Did the equation of the Least Squares Regression (LSR) line change when the units were changed? g. Graph and interpret the residual plot Only one plot necessary, use columns C1 and C2, plot the residuals against the explanatory variable. Recall: To interpret the residual plots remember that if there is a pattern in the residual plot, then the LSR line is not appropriate. If there is not a pattern residuals look random, then the LSR line is appropriate. h. Looking at the values of the correlation coefficient and the residual plot, do you think it is appropriate to use the LSR line as a model for this data set? Explain. 2. Crime Rate in the US: How does Outliers Affect the LSR Line? In columns H-J there is data (From the Statistical Abstract of the United States 2009: http://www.census.gov/compendia/statab/) for the 50 states and the District of Columbia on College: (Column C2) Percentage of the adult residents who have a college education (Bachelor's Degree or higher). Murder Rate: (Column C3) The annual number of murders per 100,000 people in the population. a. Plot the scatterplot with the fitted least squares regression line for \"college\" and \"murder rate\". Use college as the explanatory variable. b. Does any observation look like it could be influential in its effect on the regression line? c. Plot the scatterplot with the fitted line without this observation. (To remove a row of data, highlight the row and press delete. The row you should delete is for Washington D.C.) d. Comment on the change in the LSR line and the correlation. 3. Effects of health care spending. Free Response Question The Minitab Express file gives United Nations data on annual health care spending per person in 38 richer nations. The United States, at $5711 per person, is a high outlier. In addition to spending, the life expectancy at birth (in years) and infant mortality per 1000 live births.* Use these data to investigate the extent to which higher spending on health care increases life expectancy and reduces infant mortality. Support your answers with output from Minitab Express similar to the analysis you completed in problems 1 and 2. (Two comments to help explain what you find: In addition to the United States, South Africa is an outlier in scatterplots. South Africa is out of place in this group of richer nations, although it does meet the criteria that the United Nations used to make up the list. If the effects of health care spending on overall health seem small, that is in part because the data include only richer nations, most of which spend enough to ensure basic good health for their citizens.) *Note: United Nations data at hdr.undp.org/en/statistics. All amounts are in U.S. dollars at purchasing power parity. That is, the exchange rate between each currency and the dollars is set not at the fluctuating market but at the rate that gives a dollar the same buying power in each country