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




Question 1 ? Canadian Transport Accidents;Statistics Canada records the number of transport accidents involving dangerous goods;that occur in Canada every year. Transport accidents in Canada involving dangerous;goods must be reported to the government. Moreover, Statistics Canada collects data on;transport accidents involving dangerous goods across Canada and for each of the;provinces.;The spreadsheet Transport_Accidents has data on transport accidents nationally and by;province for the period from 1987 to 2011. Data are provided for all transport modes and;separately for road, rail and air. There is also a category ?Facility?, but we will not use it;in 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 distributed;across 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 to;include row and column totals.);b) Create another contingency table of Transport Mode by Province with row and column;percentages. Be sure to add appropriate labels for each of the rows and columns, not just;percentages.;c) Explain what the row percentages and column percentage mean in words. You can use;specific percentages as examples. Is it more appropriate to use row or column;percentages?;d) Does it appear that the proportion of accidents for different transport modes differ for;different provinces? Are Transport Mode and Province independent variables? Explain;your answer.;Notes;1) The spreadsheet has more data than you need for this question. Only data for 2010;and only for three transport modes (road, rail and air) should be used. Do not use data;for ?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 downloaded;from a statistical database.;3;Question 2 ? Canadian Exports (modified from Mini Case Study, p. 133);Statistics on Canadian exports are used in a variety of applications from forecasting;Canada?s gross domestic product to foreign exchange earnings to planning capacity at;Canadian ports. Monthly export data on exports for the period from January 1999 to;December 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 goods;out of Canada, while balance of payments data are based on currency exchange for goods;and services exported by Canada.;a) Using monthly data, construct four separate graphs of exports in each product category;based on the customs and the balance of payments data series. Explain what you observe;and comment on any interesting features of the four time series plots.;b) Explain what basis of calculation (customs or balance of payments) would be;appropriate for planning capacity in Canadian ports.;c) Compute annual averages for Wheat based on customs and balance of payments;monthly data. Construct a graph of exports for Wheat based on annual data (the graph;should display customs and balance of payments time series data) and comment on how;the 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 Machinery;exports based on customs data. Label your charts clearly (title, x-axis, y-axis) and choose;appropriate intervals for the histograms. Describe the resulting distributions.;e) Using monthly data, compute the mean, standard deviation, median and five-point;summary 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 customs;data and describe the scatterplot (shape, direction, strength and outliers). Compute the;correlation coefficient and comment on whether it is consistent with the scatterplot. Is;there association between Wheat and Industrial Machinery exports? Can you say that one;causes the other or vice versa?;4;Question 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 believe;this, but what do the data actually say? There are many types of crime, some worse than;others. We need a way of combining all types of crime, weighted according to how;severe the crime is.;Statistics Canada has developed a ?crime severity index? to measure the degree of crime;seriousness. More serious crimes are assigned higher weights, less serious offences are;assigned lower weights. As a result, the index reflects the overall severity of crime in a;given city (If interested, read the report referred to in the mini case study to understand;how 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 the;following questions.;a) Construct a scatterplot of Crime Severity Index on the vertical axis and Population on;the horizontal axis. Label the axes. Add the trendline.;b) State what relationship between Crime Severity Index and Population you expected to;see before constructing a scatterplot. Describe the relationship from the scatterplot.;Summarize in one or two sentences your reasoning why this type of relationship is;observed.;c) Compute the mean and standard deviation for both variables. Are the mean and the;standard deviation appropriate in summarizing the two variables? (Hint: use a histogram;to check the overall shape of the distribution for each variable).;d) Compute the correlation coefficient for the two variables. Is the correlation coefficient;consistent with the scatterplot?;e) Compute the slope and the intercept of the least-squares regression line by hand and;write the resulting regression equation. Compute the regression coefficients (slope and;intercept) using Excel and check that your results computed by hand are consistent with;the Excel output.;5;Question 4 ? Association, Correlation and Simple Linear Regression;a) 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. Fuel;consumption is measured in litres of gasoline and speed is measured in kilometers per;hour. A simple linear regression was fitted to the data, the residuals of the model were;computed and appear in the table below.;Residuals;10.09 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 3.97;Speed (x) in km/hr;65 70 75 80 85 90 95 100;105 110 115 120 125 130 135;i. 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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