2.8 What’s wrong?

Explain what is wrong with each of the following:

2.9 Make some sketches

For each of the following situations, make a scatterplot that illustrates the given relationship between two variables.

2.10 Companies of the world

In Exercise 1.118 (page 61), you examined data collected by the World Bank on the numbers of companies that are incorporated and are listed in their country’s stock exchange at the end of the year for 2012. In Exercise 1.119, you did the same for the year 2002.3 In this exercise, you will examine the relationship between the numbers for these two years.

2.11 Companies of the world

Refer to the previous exercise. Using the questions there as a guide, describe the relationship between the numbers for 2012 and 2002. Do you expect this relationship to be stronger or weaker than the one you described in the previous exercise? Give a reason for your answer.

2.12 Brand-to-brand variation in a product

Beer100.com advertises itself as “Your Place for All Things Beer.” One of their “things” is a list of 175 domestic beer brands with the percent alcohol, calories per 12 ounces, and carbohydrates (in grams).⁴ In Exercises 1.56 through 1.58 (page 36), you examined the distribution of alcohol content and the distribution of calories for these beers.

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2.13 More beer

Refer to the previous exercise. Repeat the exercise for the relationship between carbohydrates and percent alcohol. Be sure to include summaries of the distributions of the two variables you are studying.

2.14 Marketing in Canada

Many consumer items are marketed to particular age groups in a population. To plan such marketing strategies, it is helpful to know the demographic profile for different areas. Statistics Canada provides a great deal of demographic data organized in different ways.⁵

2.15 Compare the provinces with the territories

Refer to the previous exercise. The three Canadian territories are the Northwest Territories, Nunavut, and the Yukon Territories. All of the other entries in the data set are provinces.

2.16 Sales and time spent on web pages

You have collected data on 1000 customers who visited the web pages of your company last week. For each customer, you recorded the time spent on your pages and the total amount of their purchases during the visit. You want to explore the relationship between these two variables.

2.17 A product for lab experiments

Barium-137m is a radioactive form of the element barium that decays very rapidly. It is easy and safe to use for lab experiments in schools and colleges.⁶ In a typical experiment, the radioactivity of a sample of barium-137m is measured for one minute. It is then measured for three additional one-minute periods, separated by two minutes. So data are recorded at one, three, five, and seven minutes after the start of the first counting period. The measurement units are counts. Here are the data for one of these experiments:⁷

2.18 Use a log for the radioactive decay

Refer to the previous exercise. Transform the counts using a log transformation. Then repeat parts (a) through (e) for the transformed data, and compare your results with those from the previous exercise.

2.19 Time to start a business

Case 1.2 (page 23) uses the World Bank data on the time required to start a business in different countries. For Example 1.21 and several other examples that follow we used data for a subset of the countries for 2013. Data are also available for times to start in 2008. Let’s look at the data for all 189 countries to examine the relationship between the times to start in 2013 and the times to start in 2008.

2.20 Use 2003 to predict 2013

Refer to the previous exercise. The data set also has times for 2003. Use the 2003 times as the explanatory variable and the 2013 times as the response variable.

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2.21 Fuel efficiency and CO_2 emissions

Refer to Example 2.7 (pages 70–71), where we examined the relationship between CO₂ emissions and highway MPG for 1067 vehicles for the model year 2014. In that example, we used MPG as the explanatory variable and CO₂ as the response variable. Let’s see if the relationship differs if we change our measure of fuel efficiency from highway MPG to city MPG. Make a scatterplot of the fuel efficiency for city driving, city MPG, versus CO₂ emissions. Write a summary describing the relationship between these two variables. Compare your summary with what we found in Example 2.7.

2.22 Add the type of fuel to the plot

Refer to the previous exercise. As we did in Figure 2.6 (page 71), add the categorical variable, type of fuel, to your plot. (If your software does not have this capability, make separate plots for each fuel type. Use the same range of values for the y axis and for the x axis to make the plots easier to compare.) Summarize what you have found in this exercise, and compare your results with what we found in Example 2.7 (pages 70–71).