Chapter 3: Q.41 (page 191)
Acid rain Refer to Exercise . Would it be appropriate to use the regression line to predict pH after months? Justify your answer.
Short Answer
pHvalue after months is an extrapolation of the relationship.
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Chapter 3: Q.41 (page 191)
Acid rain Refer to Exercise . Would it be appropriate to use the regression line to predict pH after months? Justify your answer.
pHvalue after months is an extrapolation of the relationship.
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Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:

(a) How would change if the bones had been measured in millimeters instead of centimeters? (There are millimeters in a centimeter.)
(b) If the and variables are reversed, how would the correlation change? Explain.
Predicting tropical storms William Gray heads the Tropical Meteorology Project at Colorado State
University. His forecasts before each year鈥檚 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鈥檚 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.
What鈥檚 my grade? In Professor Friedman鈥檚 economics course, the correlation between the students鈥 total scores prior to the final examination and their final-examination scores is The pre-exam totals for all students in the course have mean and standard deviation The
final-exam scores have mean and standard deviation Professor Friedman has lost Julie鈥檚 final exam but knows that her total before the exam was He decides to predict her final-exam score from her pre-exam total.
(a) Find the equation for the appropriate least-squares regression line for Professor Friedman鈥檚 prediction. Interpret the slope of this line in context.
(b) Use the regression line to predict Julie鈥檚 final exam score.
(c) Julie doesn鈥檛 think this method accurately predicts how well she did on the final exam. Determine Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.
The National Student Loan Survey provides data on the amount of debt for recent college graduates, their current income, and how stressed they feel about college debt. A sociologist looks at the data with the goal of using the amount of debt and income to explain the stress caused by college debt.
Managing diabetes People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose
molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both HbA and FPG for diabetics five months after they had completed a diabetes education class.

(a) Make a scatterplot with HbA as the explanatory variable. There is a positive linear relationship, but it is surprisingly weak.
(b) Subject is an outlier in the y-direction. Subject is an outlier in the x-direction. Find the correlation for all subjects, for all except Subject and
for all except Subject Are either or both of these subjects influential for the correlation? Explain in simple language why r changes in opposite directions when we remove each of these points.
(c) Add three regression lines for predicting FPG from HbA to your scatterplot: for all subjects, for all except Subject and for all except Subject
Is either Subject or Subject strongly influential for the least-squares line? Explain in simple language what features of the scatterplot explain the degree of influence.
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