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Chapter 12: Q. T12.9 (page 824)

T12.9 Which of the following would provide evidence that a power model of the form y=axp, wherep鈮�0and p鈮�1, describes the relationship between a response variable y and an explanatory variable x?
a. A scatterplot of y versus x looks approximately linear.
b. A scatterplot of Iny versus x looks approximately linear.
c. A scatterplot of y versus lnx looks approximately linear.
d. A scatterplot of Iny versus lnx looks approximately linear.
e. None of these

Short Answer

Expert verified

The correct answer is option (d) A scatterplot of Inyversus Inx looks approximately linear.

Step by step solution

01

Given information

To determine the relationship between a response variable yand an explanatory variable x.

02

Explanation

Since, the explanatory Variable also known as the independent variable.

To determine which of the following would give evidence that the relationship between a response variable y and an explanatory variable xis described by a power model of the type y=axp, wherep鈮�0,p鈮�1.
As a result, if we convert both variables to their logarithms, the scatterplot of a power model becomes linear, and option (d) is the proper option, resulting in a scatterplot of Inyversus Inxthat looks approximately linear.

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Most popular questions from this chapter

Exercises T12.4鈥揟12.8 refer to the following setting. 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 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn鈥檛 perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn鈥檛 approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

26. Which of the following is the best interpretation of the value 0.4117in the computer output?

a. For each increase of 1cmin foot length, the average height increases by about0.4117cm

b. When using this model to predict height, the predictions will typically be off by about 0.4117cm.

c. The linear relationship between foot length and height accounts for 41.17%of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size 25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

When Mentos are dropped into a newly opened bottle of Diet Coke, carbon dioxide is released from the Diet Coke very rapidly, causing the Diet Coke to be expelled from the bottle. To see if using more Mentos causes more Diet Coke to be expelled, Brittany and Allie used twenty-four 2-cup bottles of Diet Coke and randomly assigned each bottle to receive either 2,3,4,or5Mentos. After waiting for the fizzing to stop, they measured the amount expelled (in cups) by subtracting the amount remaining from the original amount in the bottle. Here are their data:

Here is the computer output from a least-squares regression analysis of these data. Construct and interpret a 95%confidence interval for the slope of the true regression line.


PredictorCoefSECoefTPConstant1.00210.045122.2150.000Mentos0.07080.01235.7700.000S=0.06724R-Sq=60.2%R-Sq(adj)=58.4%

T12.2 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 transformations would be reasonable for them to try?

I. Plot the square root of the number of Cheerios against diameter.
II. Plot the cube of the number of Cheerios against diameter.
III. Plot the log of the number of Cheerios against the log of the diameter.
IV. Plot the number of Cheerios against 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

Braking distance How is the braking distance for a motorcycle related to the speed at which the motorcycle was traveling when the brake was applied? Statistics teacher Aaron Waggoner gathered data to answer this question. The table shows the speed (in miles per hour) and the distance needed to come to a complete stop when the brake was applied (in feet).

Speed (mph)Distance (ft)Speed (mph)Distance (ft)61.423252.0894.924084191848110.333044.75

a. Transform both variables using logarithms. Then calculate and state the least-squares regression line using the transformed variables.

b. Use the model from part (a) to calculate and interpret the residual for the trial when the motorcycle was traveling at 48 mph.
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