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Chapter 12: Q. 1.2 (page 751)

In Chapter 3, we examined data on the body weights and backpack weights of a group of eight randomly selected ninth-grade students at the Webb Schools. Some Minitab output from least-squares regression analysis for these data is shown.

2. With such a small sample size, it is difficult to check several of the conditions for regression inference. Assume that the conditions are met. Construct and interpret a 95%confidence interval for the slope of the population regression line.

Short Answer

Expert verified

True regression line is between(0.021525,0.160075).

Step by step solution

01

Given Information

It is given in the Question that:

02

Explanation

The sample size was reduced by 2degrees of freedom.

df=n鈭�2=8鈭�2=6

In table B, the critical t-value can be discovered in the row of df=6and the column of c=95%as follows:

t鈭�=2.447

The confidence interval is will be,

localid="1652249759789" b鈭�t*脳SEb=0.09080鈭�2.447脳0.02831=0.021525

b+t鈭�脳SEb=0.09080+2.447脳0.02831=0.160075

Therefore the true regression line lies between (0.021525,0.160075)in 95%confidence interval.

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Most popular questions from this chapter

Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value of x, the population of y-values is Normally distributed.

(b) The standard deviation 蟽of the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x. (c) The sample size鈥攖hat is, the number of paired observations (x, y)鈥攅xceeds 30.

(d) There exists a straight line y=伪+尾xsuch that, for each value of x, the mean 渭yof the corresponding population of y-values lies on that straight line.

(e) The data come from a random sample or a randomized experiment.

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 y=ax-2. 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 100-watt bulb at a distance of 2.1meters? Show your work.

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player鈥檚 total winnings from his average number of putts almost always results in errors of less than \(200,000.

(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

Which of the following would provide evidence that a power law model of the form y=axbwhere b鈮�0andb鈮�1, describes the relationship between a response variable yand an explanatory variable x.

(a) A scatterplot of yversus xlooks approximately linear.

(b) A scatterplot of ln yversus xlooks approximately linear.

(c) A scatterplot of yversus ln xlooks approximately linear.

(d) A scatterplot of ln yversus ln xlooks approximately linear.

(e) None of these.

In a clinical trial 30, patients with a certain blood disease are randomly assigned to two groups. One group is then randomly assigned the currently marketed medicine, and the other group receives the experimental medicine. Each week, patients report to the clinic where blood tests are conducted. The lab technician is unaware of the kind of medicine the patient is taking, and the patient is also unaware of which medicine he or she has been given. This design can be described as

(a) a double-blind, completely randomized experiment, with the currently marketed medicine and the experimental medicine as the two treatments.

(b) a single-blind, completely randomized experiment, with the currently marketed medicine and the experimental medicine as the two treatments.

(c) a double-blind, matched pairs design, with the currently marketed medicine and the experimental medicine forming a pair.

(d) a double-blind, block design that is not a matched pairs design, with the currently marketed medicine and the experimental medicine as the two blocks.

(e) a double-blind, randomized observational study.
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