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Chapter 3: Q 78. (page 197)
Measurements on young children in Mumbai, India, found this least-squares line for predicting height from the arm span x Measurements are in centimeters (cm).
One child in the Mumbai study had a height of and an arm spanThis child’s residual is
The correct option is (a)
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The scatter plots
Describe the direction of the relationship. Explain why this makes sense
Bird colonies Return to the data of Exercise on sparrow hawk colonies. We’ll use these data to illustrate influence.
(a) Make a scatterplot of the data suitable for predicting new adults from the percent of returning adults. Then add two new points. Point A: return,
new adults. Point B: return, new adults. In which direction is each new point an outlier?
(b) Add three least-squares regression lines to your plot: for the original colonies, for the original colonies plus Point , and for the original colonies
plus Point Which new point is more influential for the regression line? Explain in simple language why each new point moves the line in the way your graph shows.
Predicting tropical storms William Gray heads the Tropical Meteorology Project at Colorado State
University. His forecasts before each year’s hurricane season attract lots of attention. Here are data on the number of named Atlantic tropical storms predicted by Dr. Gray and the actual number of storms for the years to 2008:
Analyze these data. How accurate are Dr. Gray’s forecasts? How many tropical storms would you expect in a year when his preseason forecast calls for storms? What is the effect of the disastrous season on your answers? Follow the four-step process.
Oil and residuals The Trans-Alaska Oil Pipeline is a tube that is formed from -inch-thick steel and carries oil across miles of sensitive arctic and subarctic terrain. The pipe segments and the welds that join them were carefully examined before installation. How accurate are field measurements of the depth of small defects? The figure below compares the results of measurements on defects made in the field with measurements of the same defects made in the laboratory. The line is drawn on the scatterplot.
(a) Describe the overall pattern you see in the scatterplot, as well as any deviations from that pattern.
(b) If field and laboratory measurements all agree, then the points should fall on the line drawn on the plot, except for small variations in the measurements. Is this the case? Explain.
(c) The line drawn on the scatterplot is not the least-squares regression line. How would the slope and intercept of the least-squares line compare? Justify your answer.
Measurements on young children in Mumbai, India, found this least-squares line for predicting height from the arm span Measurements are in centimeters (cm).
According to the regression line, the predicted height of a child with an arm span of 100 cm is about
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