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Chapter 12: Q. 2 (page 759)

SAT Math scores In Chapter 3, we examined data on the percent of high school graduates in each state who took the SAT and the state's mean SAT Math score in a recent year. The figure below shows a residual plot for the least-squares regression line based on these data. Are the conditions for performing inference about the slope 尾of the population regression line met? Justify your answer.

Short Answer

Expert verified

The linear requirement has not been met.

Step by step solution

01

Given Information

Need to find which requirement has not been met.

02

Explanation

There are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random

The Linear requirement has not been met, because the residual plot contains strong curvature and thus the scatterplot is not roughly linear.

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Most popular questions from this chapter

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.

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance=490(time)2. A scatterplot of the students鈥� data showed a clear curved pattern. A scatterplot of which of the following should have a roughly linear pattern?

(a) [time, ln(distance)]

(b) [ln(time), distance]

(c) [ln(time), ln(distance)]

(d) [ln(distance), time]

(e) [distance, ln(time)]

An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69of the nearly 1000players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole and the player鈥檚 total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypotheses H0:尾=0: Ha:尾<0. The value of the t statistic for this test is

(a)2.61

(b)2.44

(c)0.081

(d)-2.44

(e) -20.24

In the casting of metal parts, molten metal flows through a 鈥済ate鈥� into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined a random sample of 12 pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process.

Construct and interpret a 95%confidence interval for the slope of the population regression line. Explain how this interval is consistent with the results of Exercise R12.2.

Park rangers are interested in estimating the weight

of the bears that inhabit their state. The rangers have data

on weight (in pounds) and neck girth (distance around

the neck in inches) for 10 randomly selected bears. Some

regression output for these data is shown below.

A bear was recently captured whose neck girth was 35inchesand whose weight was 466.35pounds. If this bear were added to the data set given above, what would be the effect on the value ofr2?

(a) It would decrease the value of r2because the added

point is an outlier.

(b) It would increase the value of r2because any point

added to the data would increase the percent of variation

in bear weight that can be explained by the least-squares

regression line.

(c) It would increase the value of r2because the added

point lies on the least-squares regression line and is far from

the point (x,y)

(d) It would have no effect on the value ofr2 because the

added point lies far from the point (x,y)

(e) It would have no effect on the value of r2because it lies

on the least-squares regression line.
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