Question 1

For the model  
= 2.72 + 2.3x,predict y when x = 5.Round to two decimal places.

Accepted Answer

A) 14.22 
B) 13.49 
C) 14.79 
D) -14.22 
E) -14.79 
A) 14.22 
B) 13.49 
C) 14.79 
D) -14.22 
E) -14.79 A

Question 2

Use technology to create a curved model for the data.

Accepted Answer

= 7.19 + 12.8 ln x

Question 3

A university radio station has been airing a public service announcement (PSA)that gives a telephone number students can call to get information on upcoming campus events.In order to determine the optimal number of times per day to run the PSA,the station has been counting the number of calls generated each day as a function of the number of times the PSA was aired.The results of the experiment are summarized in the table below.   
a)Re-express the data by squaring the number of calls per day,then plot the re-expressed data as a scatterplot.   
b)Determine the regression equation and correlation coefficient for the re-expressed data.
c)Interpret the slope of your model.Comment on the meaning and usefulness of this slope.

Accepted Answer

a)

a) b)y = 2790.1x - 1524.4,R = 0.9864 c)The slope from the model is equal to 2790.1.The units are (calls per day)<sup>2</sup> per (airings per day),which means that the square of the number of daily calls goes up 2790.1 for every additional airing per day.Taking the square root of this slope gives 52.8 calls per day per (airings per day)<sup>1/2</sup>.Neither quantity is of very much use.

b)y = 2790.1x - 1524.4,R = 0.9864
c)The slope from the model is equal to 2790.1.The units are
(calls per day)² per (airings per day),which means that the square of the number of daily calls goes up 2790.1 for every additional airing per day.Taking the square root of this slope gives 52.8 calls per day per (airings per day)^1/2.Neither quantity is of very much use.

Question 4

A company manufactures of polypropylene rope in six different sizes.To assess the strength of the ropes they test two samples of each size to see how much force (in kilograms)the ropes will hold without breaking.The table shows the results of the tests.We want to create a model for predicting the breaking strength from the diameter of the rope.Use technology to create a curved model for the data.

Accepted Answer

s @#IMG-DLM&_TB3448_11 
r = 2.

Question 5

The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below.  
What re-expression of Y should be tried as a starting point?

Accepted Answer

A) log (Y)against X 
B) 
 
Against X 
C) 
 
Against X 
D) 
 
Against X 
E) 
 
Against X 
A) log (Y)against X 
B) 
 
Against X 
C) 
 
Against X 
D) 
 
Against X 
E) 
 
Against X

Question 6

One of the important factors determining a car's fuel efficiency is its weight.This relationship is examined for 11 cars,and the association is shown in the scatterplot below.  
If a linear model is considered,the regression analysis is as follows:
Dependent variable: MPG
R-squared = 84.7%
VARIABLE COEFFICIENT
Intercept 47.1181
Weight -7.34614
The residuals plot is:  
Based upon the residuals plot,do you think that this linear model is appropriate?

Accepted Answer

A) Yes,residuals show no pattern. 
B) Yes,residuals show a linear pattern. 
C) No,residuals show a curved pattern. 
D) No,residuals show no pattern. 
E) Yes,residuals show a curved pattern. 
A) Yes,residuals show no pattern. 
B) Yes,residuals show a linear pattern. 
C) No,residuals show a curved pattern. 
D) No,residuals show no pattern. 
E) Yes,residuals show a curved pattern.

Question 7

A forester would like to know how big a maple tree might be at age 50 years.She gathers data from some trees that have been cut down,and plots the diameters (in inches)of the trees against their ages (in years).First she makes a linear model.The scatterplot and residuals plot are shown.Describe the association shown in the scatterplot.

Accepted Answer

The association between age of

Question 8

For the model  
= 4.3 + 0.1x,predict y when x = 5.Round to two decimal places.

Accepted Answer

A) 23.04 
B) 22.23 
C) 24.27 
D) 4.8 
E) 2.19 
A) 23.04 
B) 22.23 
C) 24.27 
D) 4.8 
E) 2.19

Question 9

For the model  
= 2.8  
,predict y when x = 4.Round to two decimal places.

Accepted Answer

A) 3.76 
B) 11.2 
C) 4.88 
D) 4.48 
E) 7.03 
A) 3.76 
B) 11.2 
C) 4.88 
D) 4.48 
E) 7.03

Question 10

Use technology to create a curved model for the data.

Accepted Answer

@#IMG-DLM&_TB3448_11

Question 11

For the model  
= 0.1  
+ 2.1x + 8,predict y when x = 3.Round to two decimal places.

Accepted Answer

A) 33.6 
B) 17 
C) -33.6 
D) 15.2 
E) -15.2 
A) 33.6 
B) 17 
C) -33.6 
D) 15.2 
E) -15.2

Question 12

One of the important factors determining a car's fuel efficiency is its weight.This relationship is examined for 11 cars,and the association is shown in the scatterplot below.  
If a linear model is considered,the regression analysis is as follows:
Dependent variable: MPG
R-squared = 84.7%
VARIABLE COEFFICIENT
Intercept 47.1181
Weight -7.34614
What does the slope say about this relationship?

Accepted Answer

A) Gas mileage increases an average of 7.346 mpg for each thousand pounds of weight. 
B) Gas mileage decreases an average of 7.346 mpg for each thousand pounds of weight. 
C) Gas mileage increases an average of 4.712 mpg for each thousand pounds of weight. 
D) Gas mileage decreases an average of 4.712 mpg for each thousand pounds of weight. 
E) Gas mileage decreases an average of .7346 mpg for each thousand pounds of weight. 
A) Gas mileage increases an average of 7.346 mpg for each thousand pounds of weight. 
B) Gas mileage decreases an average of 7.346 mpg for each thousand pounds of weight. 
C) Gas mileage increases an average of 4.712 mpg for each thousand pounds of weight. 
D) Gas mileage decreases an average of 4.712 mpg for each thousand pounds of weight. 
E) Gas mileage decreases an average of .7346 mpg for each thousand pounds of weight.

Question 13

For the model  
= 1.4 + 0.08 log x,predict y when x = 2.Round to two decimal places.

Accepted Answer

A) 6.72 
B) 9.4 
C) 1.42 
D) 1.56 
E) -0.94 
A) 6.72 
B) 9.4 
C) 1.42 
D) 1.56 
E) -0.94

Question 14

A forester would like to know how big a maple tree might be at age 50 years.She gathers data from some trees that have been cut down,and plots the diameters (in inches)of the trees against their ages (in years).First she makes a linear model.The scatterplot and residuals plot are shown.Do you think the linear model is appropriate? Explain.

Accepted Answer

No,the plot of residuals shows an obviou

Question 15

The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below.  
Should you re-express these data before trying to fit a model? Explain.

Accepted Answer

A) Data should be re-expressed.Scatterplot shows upward curvature and increasing scatter as X increases. 
B) Data should be re-expressed.Scatterplot shows linear relationship and uniform scatter. 
C) Data does not need to be re-expressed.Scatterplot shows upward curvature and increasing scatter as X increases. 
D) Data should be re-expressed.Scatterplot shows linear relationship. 
E) Data does not need to be re-expressed.Scatterplot shows linear relationship. 
A) Data should be re-expressed.Scatterplot shows upward curvature and increasing scatter as X increases. 
B) Data should be re-expressed.Scatterplot shows linear relationship and uniform scatter. 
C) Data does not need to be re-expressed.Scatterplot shows upward curvature and increasing scatter as X increases. 
D) Data should be re-expressed.Scatterplot shows linear relationship. 
E) Data does not need to be re-expressed.Scatterplot shows linear relationship.

Question 16

Doctors studying how the human body assimilates medication inject some patients with penicillin,and then monitor the concentration of the drug (in units/cc)in the patients' blood for seven hours.The data are shown in the scatterplot.First they tried to fit a linear model.Now the researchers try a new model,using the re-expression log(Concentration).Examine the regression analysis and the residuals plot below.Explain why you think this model is better than the original linear model.

Accepted Answer

The residuals show a

Question 17

Doctors studying how the human body assimilates medication inject a patient with penicillin,and then monitor the concentration of the drug in the patient's blood for several hours.The data are shown in the table.   
Use your model to estimate what the concentration of penicillin will be after 8 hours.

Accepted Answer

When Time = 8,log(Co @#IMG-DLM&_TB3448_1

Question 18

Doctors studying how the human body assimilates medication inject some patients with penicillin,and then monitor the concentration of the drug (in units/cc)in the patients' blood for seven hours.The data are shown in the scatterplot.First they tried to fit a linear model.The regression analysis and residuals plot are shown.Is that estimate likely to be accurate,too low,or too high? Explain.

Accepted Answer

Too high;the residua

Question 19

The consumer price index (CPI)is a measure of the relative cost of goods in a country for a particular year.The table below shows the CPI for various years beginning in 1940.   
a)Re-express the CPI by taking the log of the data,then plot the re-expressed data as a scatterplot.   
b)Determine the regression equation and correlation coefficient for the re-expressed data.
c)Use your model from part (b)to predict the CPI in 2010.