For Exercises 2.77 to 2.79, see page 101; and for 2.80, see page 102.
2.81 What's wrong?
Each of the following statements contains an error. Describe each error and explain why the statement is wrong.
2.81
(a) Whether the relationship is negative or positive does not tell us anything as to whether or not there is causation. (b) A lurking variable can be categorical. (c) It is actually impossible for all the residuals to be negative. Even if many of the residuals are negative, this tells us nothing regarding the relationship (positive or negative) of the variables. We need to look at the slope to determine if the relationship is positive or negative.
2.82 What's wrong?
Each of the following statements contains an error. Describe each error and explain why the statement is wrong.
2.83 Predict the sales
You analyzed the past 10 years of sales data for your company, and the data fit a straight line very well. Do you think the equation you found would be useful for predicting next year's sales? Would your answer change if the prediction was for sales five years from now? Give reasons for your answers.
2.83
Yes, predicting next year is reasonable. Yes, predicting 5 years from now is extrapolation.
2.84 Older workers and income
The effect of a lurking variable can be surprising when cases are divided into groups. Explain how, as a nation's population grows older, mean income can go down for workers in each age group but still go up for all workers.
2.85 Marital status and income
Data show that married, divorced, and widowed men earn quite a bit more than men the same age who have never been married. This does not mean that a man can raise his income by getting married because men who have never been married are different from married men in many ways other than marital status. Suggest several lurking variables that might help explain the association between marital status and income.
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2.86 Sales at a farmers’ market
You sell fruits and vegetables at your local farmers’ market, and you keep track of your weekly sales. A plot of the data from May through August suggests a increase over time that is approximately linear, so you calculate the least-squares regression line. Your partner likes the plot and the line and suggests that you use it to estimate sales for the rest of the year. Explain why this is probably a very bad idea.
2.87 Does your product have an undesirable side effect?
People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar. Does this mean that artificial sweeteners cause weight gain? Give a more plausible explanation for this association.
2.88 Does your product help nursing-home residents?
A group of college students believes that herbal tea has remarkable powers. To test this belief, they make weekly visits to a local nursing home, where they visit with the residents and serve them herbal tea. The nursing-home staff reports that, after several months, many of the residents are healthier and more cheerful. We should commend the students for their good deeds but doubt that herbal tea helped the residents. Identify the explanatory and response variables in this informal study. Then explain what lurking variables account for the observed association.
2.89 Education and income
There is a strong positive correlation between years of schooling completed and lifetime earnings for American men. One possible reason for this association is causation: more education leads to higher-paying jobs. But lurking variables may explain some of the correlation. Suggest some lurking variables that would explain why men with more education earn more.
2.90 Do power lines cause cancer?
It has been suggested that electromagnetic fields of the kind present near power lines can cause leukemia in children. Experiments with children and power lines are not ethical. Careful studies have found no association between exposure to electromagnetic fields and childhood leukemia.13 Suggest several lurking variables that you would want information about in order to investigate the claim that living near power lines is associated with cancer.