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mathematics
business statistics

Questions and Answers of Business Statistics

The following time series graph shows daily closing stock prices (adjusted for splits and dividends) for Google Inc. from January 1, 2008, through June 21, 2013.a) Which time series components are
The following time series graph shows daily closing stock prices for Toyota Motor Manufacturing from April 1, 2008, through June 21, 2013.a) Which time series components seem to be present? The
The Paralyzed Veterans of America (PVA) is a philanthropic organization sanctioned by the U.S. government to represent the interests of veterans who are disabled. To generate donations, the PVA sends
First Quantum Minerals Ltd., a mining and metals company based in Vancouver, produces copper, gold, and nickel. It’s listed on the Toronto and London stock exchanges. The data file
Each winter, many Canadians travel to the Caribbean for a winter vacation. Some people call them “snow birds,” including Jeff Mohammed who heads up a company offering all-inclusive packages. He
The Canadian exchange rate may be related to the TSX indices of performance of various sectors of the Canadian economy. The data file used in Exercise 25 contains monthly TSX indices for various
Exercise 27 raised some questions about the regression model built to understand the effect of OECD regulation on GDP/ Capita in 24 OECD countries. Let’s look more deeply. Here’s a histogram of
The following regression is based on weekly receipts from shows on Broadway in New York City:Dependent variable is: Receipts($M)R-squared = 93.3% R-squared (adjusted) = 93.1%s = 0.9589 with 92 = 88
Airlines strive to be on time, in part because customers can refer to government-published statistics to select f lights that are most often on time. We have data for 19 airlines for March 2006
A study by the U.S. Small Business Administration modelled the GDP per capita of 24 of the countries in the Organisation for Economic Co-operation and Development (OECD). One analysis estimated the
The price ($/lb) of lobster harvested in the Maine lobster fishing industry is an important factor in the profitability of the industry. Here is a regression model to predict the Price from the
A major sector in the Canadian economy is minerals. Growth in that sector is associated with an increase in the value of the Canadian dollar. The data set contains monthly data for the Canadian
Here are plots of two regression analyses of roller coaster Speed against Height. The first is for roller coasters that don’t have inversions and the second is for roller coasters that do.a) Would
Here is a scatterplot of the residuals from the regression in Exercise 16:a) For Behemoth, the data value for Speed is 123, and the predicted value is 130.15. If we change the data value to 124 and
Data on roller coasters at Canada’s Wonderland are available in the data file and include Speed, Height, and Number of Inversions. We performed a regression to investigate whetherSpeed is related
For the regression model in Exercise 8, the leverage values look like this:The movie with the highest leverage of 0.219 is Walt Disney’s John Carter, which grossed $66M but had a budget of $300M.
Professional sports, like many other professions, require a variety of skills for success. That makes it difficult to evaluate and predict success. Fortunately, sports provides examples we can use to
Aeroplan, the loyalty program of Air Canada, has been in operation since 1984. Travellers on Air Canada flights receive Aeroplan miles, which can be redeemed for free travel, vacations, or
Exercise 42 analyzes whether weekly earnings are related to employment opportunities in Canada. Other factors that might impact people’s weekly earnings are their number of years of education (ED)
You’ve probably heard that earnings are generally higher in urban areas than in rural areas. But why is this so? Perhaps it’s because urban areas attract a cluster of employers, producing any
EthicScan Canada monitors the social, labour, and environmental performance of 1500 companies in Canada, and makes comparisons between companies in the same industry sector. In the food industry, six
A study of the impact of the salary and stock options paid to executives of 77 Canadian companies on the company rating for corporate social responsibility (CSR) came up with the followingregression
Here are some plots of residuals for the regression of Exercise 14:Which of the regression conditions can you check with these plots? Do you find that those conditions are met? 0.30 - 0.15+ 0.00+
Here are some plots of residuals for the regression of Exercise 13:Which of the regression conditions can you check with these plots? Do you find that those conditions are met? 400 + 200 -200 + 400
In order to plan electric power generation, it is important to identify trends in generation from different sources, including wind. Statistics Canada reports the amount of renewable energy generated
A company based in Kingston, Ontario, has been installing solar modules on residential roofs in Kingston and Ottawa and is planning to expand its operation in the smaller communities along Highway
The altitude (in feet) of a Boeing 737 landing at Pearson International Airport in Toronto is shown as the average during consecutive one-minute intervals in the graph:Describe (without performing
Building permits are a leading indicator of economic growth. But do non-residential permits follow the same pattern as residential permits? Statistics Canada provides us with the requisite data in
How has the price of a lobster changed? Here’s a plot tracking the price of lobster per pound in constant year 2000 dollars:This plot isn’t straight. Would a transformation help? If so, which
How has the number of licensed lobster fishers changed? Here’s a plot of the number of Fishers vs. Year:This plot isn’t straight. Would a transformation help? If so, which one? If not, why not?
Many professions use tables to determine key quantities. The value of a log is based on the number of board feet of lumber the log may contain. (A board foot is the equivalent of a piece of wood 1
Probe a little deeper into the analysis in Exercise 49 as follows: a) Plot the data and the residuals, calculate the Durbin-Watson statistic and comment on what these imply for the regression
The data file gives quarterly gross domestic product (GDP) of Canada in billions of dollars for 1Q2000–2Q2015.a) Perform a linear regression analysis of this data.b) Interpret the slope, its
Lobster are caught in traps, which are baited and left in the open ocean. Licences to fish for lobster are limited, there is a small additional fee for each trap in use, and there are limits on the
A company selling wedding services needs to take into account the difference in age of the two partners when marketing its services. The graph shows the ages of both men and women at first marriage
The graph below shows the number of passengers travelling on major Canadian airlines month by month from November 2010 to September 2015. Time is shown as months since October 2010.a) Perform a
You probably hope your earnings will increase if you spend time studying, but by how much? Statistics Canada answers this question in the research paper from which we have reprinted the following
For the regression in Exercise 19: A student tries taking the reciprocal of customers and produces the plot shown below:a) Would you recommend this transformation? Why or why not?b) What would you
A quickly growing company shows the following scatterplot of customers vs. time (in months).a) What re-expression might you suggest for the number of customers?b) What power in the Ladder of Powers
One possible model for the manufacturing process of Exercise 17 is the following:Dependent variable is: Log (Cost per unit)R-squared = 90.1% R-squared (adjusted) = 89.3%s = 0.0841 with 15 - 2 = 13
A small company has developed an improved process for making solar panels. The company needs to set its prices and wants those prices to ref lect the efficiencies of producing larger batches. The
A study of homes that looked at the relationship between Age of a home and Price produced the following scatterplot. A regression was fit to the data, as shown:On the basis of this plot, would you
A scatterplot of Salary against Years Experience for some employees and the scatterplot of residuals against predicted Salary from the regression line are shown in the figures. On the basis of these
Trinus Pipes and Tubes, a small company in Barrie, Ontario, produces plastic pipes certified to meet the Canadian Standards Association C448 specification for use in geothermal systems. Trinus
A Canadian clothing retailer needs to test whether the content of the fabric, as stated on the label, is within acceptable limits. It outsources this work to a testing company that inspects the
Encana Corporation, whose name is an acronym for ENergy, CANada, and Alberta, is a natural gas company based in Calgary with five major natural gas operations in Canada: Bighorn, Coalbed Methane,
InterCon Travel Health is a Toronto-based company that provides services to health insurers of foreign tourists who travel to the United States and Canada.4 As described in the Guided Example in this
A treaty between the United States and Canada guarantees that one-third of the water in the Niagara River should f low over the falls. One-third can be removed from the river to generate
The Beaufort Sea, located to the north of Nunavut and the Northwest Territories, is being explored for oil and natural gas by companies that conduct geological surveys and sell the resulting data to
Exploration licences for energy companies to drill in the Beaufort Sea are overseen by Indigenous and Northern Affairs Canada. The licences typically grant the right to drill in a certain area of the
A small Canadian mining company is issuing an initial public offering (IPO) of shares on the Vancouver Stock Exchange at $17 per share. A limited number of “early” investors were able to purchase
An investor is considering how to invest her money. She has two options—either a domestic mutual fund that only invests in blue chip stocks or an international aggressive mutual fund that invests
A bicycle shop owner is deciding which products to stock. His distributor will give him a deal if he buys more of one kind of bike. The payoff table shows monthly sales for a high-end bike (selling
Akbar, of Exercises 27, 29, and 31, could obtain long-range predictions of the growing conditions for next summer. He thinks they might show a probability of good growing conditions as low as 50% or
Akbar Overgrowth, whom we met in Exercise 27, is an entrepreneur who is optimistic about the growing season. What choice should he make to maximize his return? His assistant, Lance Broadleaf, is very
Aaron, whom we met in Exercise 28, tends to be optimistic about business conditions. What is his maximax strategy that would maximize his results?In ExerciseDemand and price are related; raising
Akbar Overgrowth, from Exercise 27, estimates that the probability of a good growing season is 0.70. On that basis,In Exercise 27KickGrass Lawncare is a service that cares for lawns in a large,
Blueberries are the most important fruit in Canada. Not only do they taste good, but they also occupy over half of the land area devoted to fruit production, with blueberry exports valued at several
In potash mining, large conveyors are used underground to haul ore from the rock face to shafts through which it can be lifted to the surface for processing. A conveyer hauling one tonne per second
An organic produce company divides Canada into five regions: West, Prairies, Ontario, Quebec, and Atlantic. Each has its own greenhouses for growing organic produce and its own distribution system to
Referring to the regression in exercise 47.a) Interpret the meaning of R squared.b) Comment on how this meaning is consistent with the significance of the linear regression. Variable Coefficient
Football team owners are constantly in competition for good players. The better the winning percentage, the more likely the team will provide good business returns for the owners. Of course, the
How does the production budget of a movie depend on its length? Data on the budgets (millions of dollars) and the running times (minutes) for major-release films in a recent year are summarized in
Concern over the weather associated with El Niño has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric
For a physical exam to qualify for company-provided insurance, 14 employees had their blood pressure measured. Their systolic and diastolic BP are given here:SBP
A study of 98 investment advisors asked them to predict the value of a “penny” stock a week ahead. The correlation between the values predicted and the actual value was 0.20. Was this evidence
A website that rents movies online recorded the age and the number of movies rented during the past month for some of its customers. Here are its data:Age
For the model found in Exercise 1, predict how much a person with a household income of $75,000 would be expected to spend eating out in a week. EatOut$/wk 17.28 + 0.354 HHIncome
You’re considering opening an Estonian cuisine restaurant and wonder how much people in your target community spend on eating out relative to their household incomes. You commission a telephone
Use the data file Real-Estate to consider what factors might contribute to the price of a home. Specifically, consider:• Does the price for homes with a fireplace differ significantly from the
After emerging from bankruptcy protection in 2004, Air Canada worked with its employees at numerous measures to maintain profitability. However, its share price dropped from around $18 at the end of
A survey organization obtains the opinions of a random sample of Canadian adults as to how fair the Canadian tax system is on a five-point Likert scale, from “very fair” to “very unfair.”
A marketing executive tested two incentives to see what percentage of customers would enrol in a new web-based loyalty program. The customers were asked to log on to their accounts on the web and
With the rising costs of U.S. medical insurance and the declining interest and ability of employers to maintain proper medical coverage for their employees, business owners and employees alike are
The Carbon Disclosure Project (CDP) acts on behalf of over 700 institutional investors (pension funds, mutual funds, etc.) with almost $100 trillion of investments to collect and distribute
Nordion has developed a medical device that inserts a radioisotope inside a patient’s liver for the treatment of liver cancer. About half of the world’s liver cancer patients are in China, and
In a survey of 616 Canadian homeowners who have a wooden deck attached to their homes, Ipsos Reid found a substantial percentage had never inspected their decks for safety, 40% say they never really
Governments around the world implement measures to promote gender equality, and they need to know whether voters think they’re being successful. Angus Reid Strategies conducted a survey in Canada,
A councillor in the Vancouver Island region of Tofino proposed “discouraging the future development and location of large-format retail chains and fast-food chains.” Angus Reid Strategies
How should governments deal with crime? Should they focus on punishing criminals, or should they aim to prevent crime happening in the first place? It’s important for government policy to take
The survey described in Exercise 21 also investigated the customers’ emphasis on Quality by asking them to respond to the statement, “For the same amount of money, I will generally buy one good
The survey described in Exercise 21 also investigated the customers’ marital status. Using the same definitions for Shopping Frequency as in that exercise, the calculations yielded the following
A large company in New Brunswick that buys fish from local fisheries and distributes them to major companies and restaurants is considering launching a new ad campaign on the health benefits of fish.
A female fashion study surveyed customers to determine characteristics of the “frequent” shoppers at different department stores. Suppose you’re a marketing manager at one of the department
A sales representative who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his driving distance for several weeks and
Four professors teach Statistics at your university in classes of about 85 students each, and you need to choose a good one. You can check them out on Ratemyprofessors.com, but some professors
The IBM artificial intelligence system, Watson, achieved fame when it beat human champions at the TV trivia game Jeopardy. It works by being able to understand English text in a vast database of
Morgan Solar develops optical systems for concentrating sunlight on solar cells and sells the resulting solar systems in Southern California and other locations with intense direct sunlight. They
The experimental farm in Ottawa performs research on a wide range of crops including grains and oil seeds for farms across the country. About 30 million tonnes of wheat are produced each year in
Canola (CANada Oil Low Acid) was bred naturally at the University of Manitoba and today farms in the prairies produce about 20 million metric tonnes per year, higher than any other country in the
An airline monitors the number of seats sold in Executive class on flights from Calgary to Vancouver on weekday mornings, afternoons, and evenings, and obtains the boxplots shown below.a) What are
A wind farm is being proposed for the shore of Lake Superior to supply power to Thunder Bay and nearby mining operations. The farm operator is testing turbines from five different manufacturers and
Salmon farms in Atlantic Canada have a problem of sea lice that attack the fish. Three alternative pesticides have been developed to kill the lice and are being tested on three different farms. We
For the following experiment, indicate whether it was single-blind, double-blind, or not blinded at all. Explain your reasoning.Does a “stop smoking” program work better if it costs more? Smokers
For the following observational studies, indicate whether they are prospective or retrospective.a) An airline was concerned that new security measures might discourage air travellers. A year after
For the following observational studies, indicate whether they are prospective or retrospective.a) A company looked at a sample of returned registration cards to estimate the income level of
The Organisation for Economic Co-operation and Development (OECD) surveyed 1000 people at random in each of its member countries in 2014 and found that the number of hours worked by Canadians was
Partly as a result of a government incentive program, several businesses and residences in Ontario have installed solar panels so as to reduce their electricity bills. The amount of electricity (in
Ontario is a world leader in the installation of smart electricity meters on residences. This has allowed the province to charge different rates for electricity at different times of day and has also
The OECD conducts the Program for International Student Assessment and in 2012 tested 510,000 15-year-old high school students in 65 countries to assess their performance in math, reading, and

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