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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鈥檚 residual is
The correct option is (a)
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When it rains, it pours The figure below plots the record-high yearly precipitation in each state against that state鈥檚 record-high -hour precipitation. Hawaii is a high outlier, with a record-high yearly record of inches of rain recorded at Kukui in
(a) The correlation for all states in the figure is If we leave out Hawaii, would the correlation increase, decrease, or stay the same? Explain.
(b) Two least-squares lines are shown on the graph. One was calculated using all states, and the other omits Hawaii. Which line is which? Explain.
(c) Explain how each of the following would affect the correlation, s, and the least-squares line:
Merlins breeding Exercise (page ) gives data on the number of breeding pairs of merlins in an isolated area in each of nine years and the percent of males who returned the next year. The data show that the percent returning is lower after successful breeding seasons and that the relationship is roughly linear. The figure below shows the Minitab regression output for these data.
(a) What is the equation of the least-squares regression line for predicting the percent of males that
return from the number of breeding pairs? Use the equation to predict the percent of returning males after a season with 30 breeding pairs.
(b) What percent of the year-to-year variation in the percent of returning males is explained by the straight-line relationship with a number of breeding pairs the previous year?
(c) Use the information in the figure to find the correlation r between the percent of males that return and the number of breeding pairs. How do you know whether the sign of r is + or 鈭�?
(d) Interpret the value of s in this setting.
Measurements
on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span Measurements are in centimeters (cm).
By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is
(a) greater than zero.
(b) less than zero.
(c)
(d)
(e) Can鈥檛 tell without seeing the data.
Bird colonies Exercise examined the relationship between the number of new birds y and per cent of returning birds for sparrowhawk colonies. Here are the data once again
(a) Enter the data into your calculator and make a scatterplot.
(b) Use your calculator鈥檚 regression function to find the equation of the least-squares regression line. Add this line to your scatterplot from (a).
(c) Explain in words what the slope and intercept of the regression line tell us.
(d) An ecologist uses the line to predict how many birds will join another colony of sparrowhawks and to which of the adults from the previous year return. What鈥檚 the prediction?
Penguins diving A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study gives a scatterplot for
one penguin titled 鈥淭he Relation of Dive Duration to Depth 鈥� Duration y is measured in minutes and depth x is in meters. The report then says, 鈥淭he regression equation for this bird is:
(a) What is the slope of the regression line? Explain in specific language what this value says about this penguin鈥檚 dives.
(b) According to the regression line, how long does a typical dive to a depth of meters last?
(c) Does the intercept of the regression line make any sense? If so, interpret it. If not, explain why not.
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