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Chapter 3: Q.3.2 (page 176)
Interpret the value of this subject鈥檚 residual in context.
Residual = Observed - Predicted.
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Nahya infant weights A study of nutrition in developing countries collected data from the Egyptian
village of Nahya. Here are the mean weights (in kilograms) for infants in Nahya who were
weighed each month during their first year of life:
A hasty user of statistics enters the data into software and computes the least-squares line without plotting the data. The result is A residual plot is shown below. Would it be appropriate to use this regression line to predict from ? Justify your answer.
For the least-squares regression of fat gain on . Which of the following gives a correct interpretation of this value in context?
(a) of the points lie on the least-squares regression line.
(b) of the fat gain, values are accounted for by the least-squares line.
(c) of the variation in fat gain is accounted for by the least-squares line.
(d) of the variation in fat gain is accounted for by the least-squares line.
Smokers don鈥檛 live as long (on average) as nonsmokers, and heavy smokers don鈥檛 live as long as light smokers. You perform least-squares regression on the age at death of a group of male smokers y and the number of packs per day they smoked x. The slope of your regression line
(a) will be greater than
(b) will be less than
(c) will be equal to
(d) You can鈥檛 perform regression on these data.
(e) You can鈥檛 tell without seeing the data.
Stats teachers鈥� cars A random sample of AP Statistics teachers were asked to report the age (in years) and mileage of their primary vehicles. A scatterplot of the data, a least-squares regression printout, and a residual plot are provided below.
(a) Give the equation of the least-squares regression line for these data. Identify any variables you use.
(b) One teacher reported that her -year-old car had miles on it. Find its residual.
(c) Interpret the slope of the line in context.
(d) What鈥檚 the correlation between car age and mileage? Interpret this value in context.
(e) How well does the regression line fit the data? Justify your answer using the residual plot and s.
Beavers and beetles Do beavers benefit beetles? Researchers laid out circular plots, each meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so beetles prefer them. If so, more stumps should produce more beetle larvae. Here are the data:
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