Question 1

For the model  
= 4.16 + 7.9  
,predict y when x = 4.Round to two decimal places.

Accepted Answer

A) 130.56 
B) 19.96 
C) 35.76 
D) 0.00 
E) -11.64 
A) 130.56 
B) 19.96 
C) 35.76 
D) 0.00 
E) -11.64

Question 2

The consumer price index (CPI)is a measure of the relative cost of goods in the a given country for a particular year.The table below shows the CPI for a country for the stated years beginning in 1940.  
Re-express the CPI.Then determine the regression equation for the re-expressed data.Use your model to predict the CPI in 2,017.

Accepted Answer

A) 289.3 
B) 277 
C) 296.5 
D) 261.2 
E) 241.8 
A) 289.3 
B) 277 
C) 296.5 
D) 261.2 
E) 241.8

Question 3

QuarkNet,a project funded by the National Science Foundation and the U.S.Department of Energy,poses the following problem on its website:
"Last year,deep within the Soudan mine,QuarkNet teachers began a long-term experiment to measure the amount of carbon-14 remaining in an initial 100-gram sample at 2000-year intervals.The experiment will be complete in the year 32001.Fortunately,a method for sending information backwards in time will be discovered in the year 29998,so,although the experiment is far from over,the results are in."
Here is a portion of the data:   
A scatterplot of these data looks like:   
Straighten the scatterplot by re-expressing these data and create an appropriate model for predicting the mass from the year.

Accepted Answer

Re-express the data using Time

Question 4

The relationship between two quantities x and y is examined,and the association is shown in the scatterplot below.  
Describe the association between these variables shown in the scatterplot.

Accepted Answer

A) Fairly linear,weak relationship 
B) Fairly exponential,strong relationship 
C) Fairly linear,strong relationship 
D) Fairly exponential,weak relationship 
E) Fairly quadratic,weak relationship 
A) Fairly linear,weak relationship 
B) Fairly exponential,strong relationship 
C) Fairly linear,strong relationship 
D) Fairly exponential,weak relationship 
E) Fairly quadratic,weak relationship

Question 5

Dioxins are a class of long-lived and highly toxic pollutants.The topsoil concentration in parts per million (ppm)are shown in the table below as a function of distance from the dump.  
Create an appropriate model to re-express the concentration (ppm).Then determine the regression equation and correlation coefficient for the re-expressed data.Round all figures to 4 decimal places.

Accepted Answer

A) Re-expression:
 
;y = .0012x + 0.0218,r = 0.9985 
B) Re-expression:
 
;y = .0012x + .0500,r = 1 
C) Re-expression:
 
;y = .0012x + 0.0233,r = 0.9970 
D) Re-expression:
 
;y = .0012x + 0.0251,r = 0.9928 
E) Re-expression:
 
;y = .0012x + 0.0277,r = 0.9873 
A) Re-expression:
 
;y = .0012x + 0.0218,r = 0.9985 
B) Re-expression:
 
;y = .0012x + .0500,r = 1 
C) Re-expression:
 
;y = .0012x + 0.0233,r = 0.9970 
D) Re-expression:
 
;y = .0012x + 0.0251,r = 0.9928 
E) Re-expression:
 
;y = .0012x + 0.0277,r = 0.9873

Question 6

QuarkNet,a project funded by the National Science Foundation and the U.S.Department of Energy,poses the following problem on its website:
"Last year,deep within the Soudan mine,QuarkNet teachers began a long-term experiment to measure the amount of carbon-14 remaining in an initial 100-gram sample at 2000-year intervals.The experiment will be complete in the year 32001.Fortunately,a method for sending information backwards in time will be discovered in the year 29998,so,although the experiment is far from over,the results are in."
Here is a portion of the data:   
A scatterplot of these data looks like:   
Use your model to estimate what the mass will be after 7500 years.

Accepted Answer

log(M @#IMG-DLM&_TB3448_11 
ss)= 2.00143

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.Now she re-expresses the data,using the logarithm of age to try to predict the diameter of the tree.Here are the regression analysis and the residuals plot.Using this model,predict the diameter of a maple tree at age 50 years.

Accepted Answer

Model: Di @#IMG-DLM&_TB3448_11 
m = -8.6

Question 8

The consumer price index (CPI)is a measure of the relative cost of goods in the a given country for a particular year.The table below shows the CPI for a country for the stated years beginning in 1940.  
Re-express the CPI.Then determine the regression equation and correlation coefficient for the re-expressed data.

Accepted Answer

A) Re-expression: log(CPI);y = 0.0184x - 34.5699,r = 0.9874 
B) Re-expression: - log(CPI);y = -0.0184x - 34.5699,r = 0.9780 
C) Re-expression:
 
;y = 0.0295x - 32.2299,r = 0.9874 
D) Re-expression: -
 
;y = 0.0755x - 36.9099,r = 0.9856 
E) Re-expression:
 
;y = 0.0184x - 34.5699,r = 1.0379 
A) Re-expression: log(CPI);y = 0.0184x - 34.5699,r = 0.9874 
B) Re-expression: - log(CPI);y = -0.0184x - 34.5699,r = 0.9780 
C) Re-expression:
 
;y = 0.0295x - 32.2299,r = 0.9874 
D) Re-expression: -
 
;y = 0.0755x - 36.9099,r = 0.9856 
E) Re-expression:
 
;y = 0.0184x - 34.5699,r = 1.0379

Question 9

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.Find a model that uses re-expressed data to straighten the scatterplot.

Accepted Answer

@#IMG-DLM&_TB3448_11 = 2.64 +

Question 10

Dioxins are a class of long-lived and highly toxic pollutants.The topsoil concentration of dioxins in parts per million (ppm)are shown in the table below as a function of the distance from the dump.   
a)Re-express the dioxin concentration by taking the reciprocal square root 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 dioxin concentration at a distance of 500 metres.

Accepted Answer

a) @#IMG-DLM&_TB3448_00 
 @#IMG-DLM&_TB3448_00 
b)

Question 11

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.Now she re-expresses the data,using the logarithm of age to try to predict the diameter of the tree.Here are the regression analysis and the residuals plot.Explain why you think this is a better model.

Accepted Answer

There is n

Question 12

The consumer price index (CPI)is a measure of the relative cost of goods in the a given country for a particular year.The table below shows the CPI for a country for the stated years beginning in 1940.  
Create an appropriate model to re-express the CPI.What re-expression of the CPI does this model involve?

Accepted Answer

A) -
  
B) 
  
C) log (CPI) 
D) 
  
E) 
  
A) -
  
B) 
  
C) log (CPI) 
D) 
  
E)

Question 13

The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below.  
If a linear model is considered,the regression analysis is as follows:
Dependent variable: Y
R-squared = 84.7%
VARIABLE COEFFICIENT
Intercept 1.2305
X .4443
What does the slope say about this relationship?

Accepted Answer

A) For every increase in X of 1,the corresponding average increase in Y is .4443 
B) For every increase in X of .5,the corresponding average decrease in Y is .4443 
C) For every increase in X of .5,the corresponding average increase in Y is .4443 
D) For every increase in X of 1,the corresponding average increase in Y is 1.2305 
E) For every increase in X of 1,the corresponding average decrease in Y is .4443 
A) For every increase in X of 1,the corresponding average increase in Y is .4443 
B) For every increase in X of .5,the corresponding average decrease in Y is .4443 
C) For every increase in X of .5,the corresponding average increase in Y is .4443 
D) For every increase in X of 1,the corresponding average increase in Y is 1.2305 
E) For every increase in X of 1,the corresponding average decrease in Y is .4443

Question 14

Dioxins are a class of long-lived and highly toxic pollutants.The topsoil concentration in parts per million (ppm)are shown in the table below as a function of distance from the dump.  
Create an appropriate model to re-express the concentration (ppm).What re-expression of the concentration (ppm)does this model involve?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) log (ppm) 
A) 
  
B) 
  
C) 
  
D) 
  
E) log (ppm)

Question 15

The model  
= 3.30 + 0.235(speed)can be used to predict the stopping distance (in centimetres)for a car traveling at a specific speed (in km/h).According to this model,about how much distance will a car going 65 km/h need to stop?

Accepted Answer

A) 345.0 cm 
B) 729.0 cm 
C) 4.3 cm 
D) 18.6 cm 
E) 27.0 cm 
A) 345.0 cm 
B) 729.0 cm 
C) 4.3 cm 
D) 18.6 cm 
E) 27.0 cm

Question 16

For the model ln  
= 3.21 + 8.1x,predict y when x = 5.Round to two decimal places.

Accepted Answer

A) 1.64 
B) 43.71 
C) 9,616,384,107,947,345,920.00 
D) 
 
Is undefined for x = 5. 
E) 3.78 
A) 1.64 
B) 43.71 
C) 9,616,384,107,947,345,920.00 
D) 
 
Is undefined for x = 5. 
E) 3.78

Question 17

For the model log  
= 2.1 + 0.5x,predict y when x = 2.Round to two decimal places.

Accepted Answer

A) 158,489.32 
B) 1,267.63 
C) 1,258.93 
D) 1,274.13 
E) 0.49 
A) 158,489.32 
B) 1,267.63 
C) 1,258.93 
D) 1,274.13 
E) 0.49

Question 18

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.  
Describe the association between these variables shown in the scatterplot.

Accepted Answer

A) Fairly Exponential,positive,strong relational 
B) Fairly Quadratic,positive,weak relationship 
C) Fairly linear,negative,strong relationship 
D) Fairly linear,negative,weak relationship 
E) Fairly linear,positive,strong relationship 
A) Fairly Exponential,positive,strong relational 
B) Fairly Quadratic,positive,weak relationship 
C) Fairly linear,negative,strong relationship 
D) Fairly linear,negative,weak relationship 
E) Fairly linear,positive,strong relationship

Question 19

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 information above,what re-expression of Y would be appropriate?

Accepted Answer

A) log y gallons per mile 
B) 100 ∙
 
Gallons per 100 miles 
C) -100 ∙
 
Gallons per 100 miles 
D) 100 ∙
 
Gallons per 100 miles 
E) 100 ∙
 
Gallons per 100 miles 
A) log y gallons per mile 
B) 100 ∙
 
Gallons per 100 miles 
C) -100 ∙
 
Gallons per 100 miles 
D) 100 ∙
 
Gallons per 100 miles 
E) 100 ∙
 
Gallons per 100 miles

Question 20

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.The company is thinking of introducing a new 25 mm rope.How strong should it be? (Write a sentence in context based on one of your models. )

Accepted Answer

The model estimates this rope

For the model = 4.16 + 7.9 ,predict y when x = 4.Round to two decimal places.

The relationship between two quantities x and y is examined,and the association is shown in the scatterplot below. Describe the association between these variables shown in the scatterplot.

The model = 3.30 + 0.235(speed)can be used to predict the stopping distance (in centimetres)for a car traveling at a specific speed (in km/h).According to this model,about how much distance will a car going 65 km/h need to stop?

For the model ln = 3.21 + 8.1x,predict y when x = 5.Round to two decimal places.

For the model log = 2.1 + 0.5x,predict y when x = 2.Round to two decimal places.

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. Describe the association between these variables shown in the scatterplot.

Data

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Surveys

From Randomness to Probability

Probability Rules

Random Variables

Probability Models

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

Exam 9: Re-Expressing Data: Get It Straight