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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

The swinging pendulum Mrs. Hanrahan鈥檚 precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulum鈥檚 length and its period is

period=2蟺glength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

Expose marine bacteria to X-rays for time periods from 1to 15minutes. Here are the number of surviving bacteria (in hundreds) on a culture plate after each exposure time.

TimetCountyTimetCounty1355956221110383197113641661232514213216106141971041515860

(a) Make a reasonably accurate scatterplot of the data by hand, using time as the explanatory variable. Describe what you see.

(b) A scatterplot of the natural logarithm of the number of surviving bacteria versus time is shown below. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between the count of bacteria and time.

Minitab output from a linear regression analysis on the transformed data is shown below.

PredictorCoefSE CoefTPConstant5.973160.0597899.920.000Time-0.2184250.006575-33.220.000

S=0.110016R-Sq=98.8%R-Sq(adj)=98.7%

Give the equation of the least-squares regression line. Be sure to define any variables you use.

(d) Use your model to predict the number of surviving bacteria after 17minutes. Show your work. Do you expect this prediction to be too high, too low, or about right? Explain

The slope 尾 of the population regression line describes

(a) the exact increase in the selling price of an individual unit when its appraised value increases by \(1000

(b) the average increase in the appraised value in a population of units when the selling price increases by \)51000.

(c) the average increase in selling price in a population of units when the appraised value increases by \( 1000.

(d) the average selling price in a population of units when a unit's appraised value is 0.

(e) the average increase in appraised value in a sample of 16 units when the selling price increases by \) 1000.

Color words (1.3) Do the data provide evidence of a difference in the average time required to perform the two tasks? Include an appropriate graph and numerical summaries in your answer.

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

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(b)2.44

(c)0.081

(d)-2.44

(e) -20.24
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