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Chapter 3: Q 40. (page 203)
Residual gas Refer to Exercise 38. During March, the average temperature was 46.4掳F and Joan used an average of 490 cubic feet of gas per day. Calculate and interpret the residual for this month.
Residual is
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Managing diabetes People with diabetes measure their fasting plasma glucose (FPG, measured in 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 gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.
a. Make a scatterplot with HbA as the explanatory variable. Describe what you see.
b. Subject 18 is an outlier in the x-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.
c. Subject 15 is an outlier in the y-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.
Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person鈥檚 weight leaving out all fat. Metabolic rate is measured in calories burned per hours. The researchers believe that lean body mass is an
important influence on metabolic rate.
a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.
b. Describe the relationship between lean body mass and metabolic rate.
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 exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julie鈥檚 final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.
a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.
b. Use the least-squares regression line to predict Julie鈥檚 final exam score.
c. Explain the meaning of the phrase 鈥渓east squares鈥� in the context of this question.
d. Julie doesn鈥檛 think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.
Manatees are large, gentle, slow-moving sea creatures found along the coast of Florida. Many manatees are injured or killed by boats. Here is a scatterplot showing the relationship between the number of boats registered in Florida (in thousands) and the number of manatees killed by boats for the years to Closer to Explain your reasoning.
More long jumps Refer to Exercise 52. Use technology to create a residual plot. Sketch the residual plot and explain what information it provides.
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