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COMM 291 ASSIGNMENT 2 - Application of Statistics in Business (Fall 2014) 4 Problems Set

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Question;Question 1 ? Canadian Transport AccidentsStatistics Canada records the number of transport accidents involving dangerous goodsthat occur in Canada every year. Transport accidents in Canada involving dangerousgoods must be reported to the government. Moreover, Statistics Canada collects data ontransport accidents involving dangerous goods across Canada and for each of theprovinces.The spreadsheet Transport_Accidents has data on transport accidents nationally and byprovince for the period from 1987 to 2011. Data are provided for all transport modes andseparately for road, rail and air. There is also a category ?Facility?, but we will not use itin this assignment.a) Using data in the spreadsheet, construct a contingency table of Transport Mode(columns) by Province/Territories (rows), which will show how accidents are distributedacross the three modes of transport and across different provinces for the year of 2010(Hint: include only three modes of transport (road, rail and air) and don?t forget toinclude row and column totals.)b) Create another contingency table of Transport Mode by Province with row and columnpercentages. Be sure to add appropriate labels for each of the rows and columns, not justpercentages.c) Explain what the row percentages and column percentage mean in words. You can usespecific percentages as examples. Is it more appropriate to use row or columnpercentages?d) Does it appear that the proportion of accidents for different transport modes differ fordifferent provinces? Are Transport Mode and Province independent variables? Explainyour answer.Notes:1) The spreadsheet has more data than you need for this question. Only data for 2010and only for three transport modes (road, rail and air) should be used. Do not use datafor ?Facility?.2) Use Excel?s pivot tables to extract data for 2010.3) This problem is designed to show students how to work with ?raw? data downloadedfrom a statistical database.3Question 2 ? Canadian Exports (modified from Mini Case Study, p. 133)Statistics on Canadian exports are used in a variety of applications from forecastingCanada?s gross domestic product to foreign exchange earnings to planning capacity atCanadian ports. Monthly export data on exports for the period from January 1999 toDecember 2008 are contained in the spreadsheet Canadian_Exports.These data are sourced from Statistics Canada for four selected products: wheat, zinc,fertilizer and industrial machinery. Exports are computed both based on ?customs? and?balance of payments? statistics. Customs data are based on physical movement of goodsout of Canada, while balance of payments data are based on currency exchange for goodsand services exported by Canada.a) Using monthly data, construct four separate graphs of exports in each product categorybased on the customs and the balance of payments data series. Explain what you observeand comment on any interesting features of the four time series plots.b) Explain what basis of calculation (customs or balance of payments) would beappropriate for planning capacity in Canadian ports.c) Compute annual averages for Wheat based on customs and balance of paymentsmonthly data. Construct a graph of exports for Wheat based on annual data (the graphshould display customs and balance of payments time series data) and comment on howthe time series plot based on monthly data differs from the plot based on annual data.d) Using monthly data, construct two histograms of Wheat and Industrial Machineryexports based on customs data. Label your charts clearly (title, x-axis, y-axis) and chooseappropriate intervals for the histograms. Describe the resulting distributions.e) Using monthly data, compute the mean, standard deviation, median and five-pointsummary for each of Wheat and Industrial Machinery exports based on customs data.Report your results in a properly labeled table.f) Create a scatterplot of exports of Wheat versus Industrial Machinery based on customsdata and describe the scatterplot (shape, direction, strength and outliers). Compute thecorrelation coefficient and comment on whether it is consistent with the scatterplot. Isthere association between Wheat and Industrial Machinery exports? Can you say that onecauses the other or vice versa?4Question 3 ? Crime in Canada (modified from Mini Case Study, p. 171)Is crime worse in larger cities compared to smaller ones? Many people tend to believethis, but what do the data actually say? There are many types of crime, some worse thanothers. We need a way of combining all types of crime, weighted according to howsevere the crime is.Statistics Canada has developed a ?crime severity index? to measure the degree of crimeseriousness. More serious crimes are assigned higher weights, less serious offences areassigned lower weights. As a result, the index reflects the overall severity of crime in agiven city (If interested, read the report referred to in the mini case study to understandhow the index is computed).The spreadsheet Crime_in_Canada has the crime severity index and the population size(in thousands) for select cities in Canada. Use the data in the spreadsheet to answer thefollowing questions.a) Construct a scatterplot of Crime Severity Index on the vertical axis and Population onthe horizontal axis. Label the axes. Add the trendline.b) State what relationship between Crime Severity Index and Population you expected tosee before constructing a scatterplot. Describe the relationship from the scatterplot.Summarize in one or two sentences your reasoning why this type of relationship isobserved.c) Compute the mean and standard deviation for both variables. Are the mean and thestandard deviation appropriate in summarizing the two variables? (Hint: use a histogramto check the overall shape of the distribution for each variable).d) Compute the correlation coefficient for the two variables. Is the correlation coefficientconsistent with the scatterplot?e) Compute the slope and the intercept of the least-squares regression line by hand andwrite the resulting regression equation. Compute the regression coefficients (slope andintercept) using Excel and check that your results computed by hand are consistent withthe Excel output.5Question 4 ? Association, Correlation and Simple Linear Regressiona) State whether the following statement is true or false. Explain your answer.i. The correlation of -0.78 shows that there is almost no association between a country?s GDP and Infant Mortality Rate. ii. The correlation of -0.78 between GDP and Infant Mortality Rate implies that the correlation between Infant Mortality Rates and GDP is 0.78.iii. The correlation between GDP and Country is 0.44, showing a positive linear relationship between the two variables. iv. A very high correlation (r = 1.5) is observed between a country?s per capita GDP and Living Standard Index.b) Data on fuel consumption (y) of a car at various speeds (x) were collected. Fuelconsumption is measured in litres of gasoline and speed is measured in kilometers perhour. A simple linear regression was fitted to the data, the residuals of the model werecomputed and appear in the table below.Residuals10.09 2.24 -0.62 -2.47 -3.33 -4.28 -3.73 -2.94-2.17 -1.32 -0.42 0.57 1.64 2.76 3.97Speed (x) in km/hr65 70 75 80 85 90 95 100105 110 115 120 125 130 135i. Make a scatterplot of the residuals versus speed. Describe the scatterplot. ii. Compute the mean of the residuals. Explain why you get this result.iii. Would you use the estimated linear regression line to predict fuel consumption based on speed? Explain your answer.

 

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