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Chapter 12: Q. 6 (page 760)
6. Beer and BAC Refer to Exercise 4. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.
The model for regression inference has three parameters:Explain what each parameter represents in context. Then provide an estimate for each.
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Determining tree biomass It is easy to measure the 鈥渄iameter at breast height鈥� of a tree. It鈥檚 hard to measure the total 鈥渁boveground biomass鈥� of a tree, because to do this you must cut and weigh the tree. The biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. Combining data on trees in tropical rain forests gives this relationship between biomass measured in kilograms and diameter x measured in centimeters:
Inference about the slope of a least-squares regression line is based on which of the following distributions?
(a) The t distribution with degrees of freedom
(b) The standard Normal distribution
(c) The chi-square distribution with degrees of freedom
(d) The t distribution with degrees of freedom
(e) The Normal distribution with mean and standard deviation
Side effects A drug manufacturer claims that less than 10 % of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300 out of 5000 Alzheimer's patients whose families have given informed consent for the patients to participate in the study. In all, 25 of the subjects experience nausea. Use these data to perform a test of the drug manufacturer's claim at the significance level.
In physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. A scatterplot of the data is shown below. Note that a candela (cd) is a unit of luminous intensity in the International System of Unit
Physics textbooks suggest that the relationship between light intensity y and distance x should follow an 鈥渋nverse square law,鈥� that is, a power-law model of the form . We transformed the distance measurements by squaring them and then taking their reciprocals. Some computer output and a residual plot from a least-squares regression analysis on the transformed data are shown below. Note that the horizontal axis on the residual plot displays predicted light intensity
(a) Did this transformation achieve linearity? Give appropriate evidence to justify your answer.
(b) What would you predict for the intensity of a -watt bulb at a distance of meters? Show your work.
Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.
The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?
I. Take the square root of the number of Cheerios.
II. Cube the number of Cheerios.
III. Take the log of the number of Cheerios.
IV. Take the log of the diameter.
(a) I and II
(b) I and III
(c) II and III
(d) II and IV
(e) I and IV
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