Question 1

If a data set has a relationship that is best described by a linear model, than the residual plot will

Accepted Answer

A)  be an unknown shape. 
B)  have no pattern with a correlation near 0. 
C)  none of these 
D)  also have a linear pattern with a similar correlation. 
E)  have a curved pattern, like a parabola. 
A)  be an unknown shape. 
B)  have no pattern with a correlation near 0. 
C)  none of these 
D)  also have a linear pattern with a similar correlation. 
E)  have a curved pattern, like a parabola.

Question 2

Researchers studying growth patterns of children collect data on the heights of fathers and sons.
The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely
To be . . .

Accepted Answer

A)  near +0.7 
B)  near +1.0 
C)  near -1.0 
D)  near 0 
E)  somewhat greater than 1.0 
A)  near +0.7 
B)  near +1.0 
C)  near -1.0 
D)  near 0 
E)  somewhat greater than 1.0

Question 3

A plot of the residuals versus the fitted values for record-breaking times of female
marathon runners for the years 1998 - 2003 is:   
Based on this residuals plot, does it seem reasonable to use linear regression for this
model? Explain.

Accepted Answer

Since we see a clear pattern i

Question 4

Which statement about re-expressing data is not true?
I. Unimodal distributions that are skewed to the left will be made more symmetric by taking the
Square root of the variable.
II. A curve in which the direction of the association changes from negative to positive
Will not benefit from re-expression.
III. One goal of re-expression may be to make the variability of the response variable more
Uniform.

Accepted Answer

A)  III only 
B)  I, II, and III 
C)  II only 
D)  II and III 
E)  I only 
A)  III only 
B)  I, II, and III 
C)  II only 
D)  II and III 
E)  I only

Question 5

A study examined the number of trees in a variety of orange groves and the corresponding number of oranges that each
grove produces in a given harvest year. Linear regression was calculated and the results are below. linear regression results:
Dependent Variable: oranges Independent Variable: trees
Sample size: 9
$$
\begin{array}{l}
\mathrm{R}-\mathrm{sq}=0.886 \
\mathrm{~s}=31394.7
\end{array}
$$

$\begin{array}{|l|r|r|}
\hline \text { Parameter } & \text { Estimate } & \text { Std. Err. } \
\hline \text { Constant } & 390.59 & 16328.8 \
\hline \text { Trees } & 525.84 & 71.22 \
\hline
\end{array}$

-If these data were collected in California, would you feel confident in using this equation to
make predictions about Florida orange groves also? Explain.

Accepted Answer

No. It would be a dangerous as

Question 6

In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail,
the data were gathered from the United States Postal Service. In 1981, the United States Postal Service changed their rates on
March 22 and November 1. This information is shown in the table. $$\begin{array} { | l | l | } 
\hline \text { Year } & \text { Rate } \
\hline 1971 & 0.08 \
\hline 1974 & 0.10 \
\hline 1975 & 0.13 \
\hline 1978 & 0.15 \
\hline 1981 & 0.18 \
\hline 1981 & 0.20 \
\hline 1985 & 0.22 \
\hline 1988 & 0.25 \
\hline 1991 & 0.29 \
\hline 1995 & 0.32 \
\hline
\end{array}$$
-Interpret the slope of your model in context.

Accepted Answer

Slope of model is 0.0101518. T

Question 7

In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail,
the data were gathered from the United States Postal Service. In 1981, the United States Postal Service changed their rates on
March 22 and November 1. This information is shown in the table. $$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Rate } \
\hline 1971 & 0.08 \
\hline 1974 & 0.10 \
\hline 1975 & 0.13 \
\hline 1978 & 0.15 \
\hline 1981 & 0.18 \
\hline 1981 & 0.20 \
\hline 1985 & 0.22 \
\hline 1988 & 0.25 \
\hline 1991 & 0.29 \
\hline 1995 & 0.32 \
\hline
\end{array}$$
-Interpret the intercept of your model in context.

Accepted Answer

Intercept of the model is @#LAT-DLM&. Th

Question 8

Residuals are . . .

Accepted Answer

A)  variation in the data that is explained by the model. 
B)  possible models not explored by the researcher. 
C)  none of these 
D)  the difference between observed responses and values predicted by the model. 
E)  data collected from individuals that is not consistent with the rest of the group. 
A)  variation in the data that is explained by the model. 
B)  possible models not explored by the researcher. 
C)  none of these 
D)  the difference between observed responses and values predicted by the model. 
E)  data collected from individuals that is not consistent with the rest of the group.

Question 9

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from
500 to 1000, how much do we predict he will increase his electric bill by?

Accepted Answer

A)  $22.50 
B)  $35 
C)  $12.50 
D)  $2 
E)  $10 
A)  $22.50 
B)  $35 
C)  $12.50 
D)  $2 
E)  $10

Question 10

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD).
The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004: $\begin{array}{|c|c|}
\hline 2004 \text { US \$ } & \text { Carat } \
\hline 494.82 & 0.12 \
\hline 768.03 & 0.17 \
\hline 1105.03 & 0.20 \
\hline 1508.88 & 0.25 \
\hline 1826.18 & 0.28 \
\hline 2096.89 & 0.33 \
\hline
\end{array}$

$\begin{array}{|c|c|}
\hline 2004 \text { US\$ } & \text { Carat } \
\hline 688.24 & 0.15 \
\hline 944.90 & 0.18 \
\hline 1071.75 & 0.21 \
\hline 1504.44 & 0.26 \
\hline 1908.28 & 0.29 \
\hline 2409.76 & 0.35 \
\hline
\end{array}$

$\begin{array}{|c|c|}
\hline \text { 2004 US \$ } & \text { Carat } \
\hline 748.10 & 0.16 \
\hline 1076.18 & 0.19 \
\hline 1289.20 & 0.23 \
\hline 1597.63 & 0.27 \
\hline 2038.09 & 0.32 \
\hline & \
\hline
\end{array}$

-Interpret the intercept of your model in context.

Accepted Answer

The intercept of the model is

Question 11

On the axes below, sketch a scatterplot described: a. a strong negative association

b. a strong association but $r$ is near 0

c. a weak but positive association

Accepted Answer

The answer of On the axes below, sketch a scatterplot...

Question 12

A consumer group collected information on HDTVs . They created a linear model to estimate the
Cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the
Slope of the line of best fit?

Accepted Answer

A)  7 
B)  7000 
C)  70 
D)  0.70 
E)  700 
A)  7 
B)  7000 
C)  70 
D)  0.70 
E)  700

Question 13

Storks Data show that there is a positive association between the population of 17
European countries and the number of stork pairs in those countries.
a. Briefly explain what "positive association" means in this context.
b. Wildlife advocates want the stork population to grow, and jokingly suggest that citizens
should be encouraged to have children. As a statistician, what do you think of this
suggestion? Explain briefly.

Accepted Answer

a. Positive association implies that cou

Question 14

The correlation coefficient between the hours that a person is awake during a 24-hour period and
The hours that same person is asleep during a 24-hour period is most likely to be

Accepted Answer

A)  near +0.8 
B)  near 0 
C)  near -0.8 
D)  exactly -1.0 
E)  exactly +1.0 
A)  near +0.8 
B)  near 0 
C)  near -0.8 
D)  exactly -1.0 
E)  exactly +1.0

Question 15

Current research states that a good diet should contain 20-35 grams of dietary fiber. Research also states that each day should
start with a healthy breakfast. The nutritional information for 77 breakfast cereals was reviewed to find the grams of fiber and
the number of calories per serving. The scatterplot below shows the relationship between fiber and calories for the cereals.  
-Do you think a model could accurately predict the number of calories in a serving of cereal
that has 22 grams of fiber? Explain.

Accepted Answer

This data contains information about cer

Question 16

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars.  
-Describe why performing linear regression with these data is not a good decision.

Accepted Answer

The data is clearly

Question 17

All but one of these statements contain a mistake. Which could be true?

Accepted Answer

A)  The correlation between the amount of fertilizer used and the yield of beans is 0.42. 
B)  There is a correlation of 0.63 between gender and political party. 
C)  The correlation between a football player's weight and the position he plays is 0.54. 
D)  There is a high correlation (1.09) between height of a corn stalk and its age in weeks. 
E)  The correlation between a car's length and its fuel efficiency is 0.71 miles per gallon. 
A)  The correlation between the amount of fertilizer used and the yield of beans is 0.42. 
B)  There is a correlation of 0.63 between gender and political party. 
C)  The correlation between a football player's weight and the position he plays is 0.54. 
D)  There is a high correlation (1.09) between height of a corn stalk and its age in weeks. 
E)  The correlation between a car's length and its fuel efficiency is 0.71 miles per gallon.

Question 18

Breaking strength A company manufactures 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. $$\begin{array} { | c | c : c | } 
\hline \begin{array} { c } 
\text { Diameter } \
( \mathrm { mm } )
\end{array} & \begin{array} { c } 
\text { Strength } \
( \mathrm { kg } )
\end{array} \
\hline 4 & 60 & 76 \
\hline 7 & 157 & 153 \
\hline 10 & 254 & 262 \
\hline 12 & 334 & 388 \
\hline 15 & 551 & 529 \
\hline 20 & 938 & 893 \
\hline
\end{array}$$ 
a. Find a model that uses re-expressed data to straighten the scatterplot.
b. The company is thinking of introducing a new 25mm rope. How strong should it be?
(Write a sentence in context based on one of your models.)

Accepted Answer

a. @#LAT-DLM& b. The model estimates thi

Question 19

Gas mileage again In the Data Desk lab last week you analyzed the association between a
car's fuel economy and its weight. Another important factor in the amount of gasoline a car
uses is the size of the engine. Called "displacement", engine size measures the volume of
the cylinders in cubic inches. The regression analysis is shown. Dependent variable is:
MPG
89 total cases of which 0 are missing
R squared $= 60.9 \% \quad$ R squared (adjusted) $= 60.0 \%$
$\mathrm { s } = 3.056$ with $89 - 2 = 87$ degrees of freedom

$\begin{array}{llrrr}
\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \
\text { Regression } & 696.744 & 1 & 696.744 & 74.6 \
\text { Residual } & 448.236 & 48 & 9.33826 &
\end{array}$

$\begin{array}{lllll}
\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \
\text { Constant } & 34.9799 & 1.231 & 28.4 & \text { Š } 0.0001 \
\text { Eng. Displcmt } & -0.066196 & 0.0077 & -8.64 & \text { S } 0.0001
\end{array}$

a. How many cars were included in this analysis?
b. What is the correlation between engine size and fuel economy?
c. A car you are thinking of buying is available with two different size engines, 190 cubic
inches or 240 cubic inches. How much difference might this make in your gas mileage?
(Show work)

Accepted Answer

a) 89
b) @#LAT-DLM&

Question 20

Which statement about residuals plots is true?
I. A curved pattern indicates nonlinear association between the variables.
II. A pattern of increasing spread indicates the predicted values become less reliable as the
Explanatory variable increases.
III. Randomness in the residuals indicates the model will predict accurately.

Accepted Answer

A)  I and III only 
B)  II only 
C)  I, II, and III 
D)  I and II only 
E)  I only 
A)  I and III only 
B)  II only 
C)  I, II, and III 
D)  I and II only 
E)  I only

If a data set has a relationship that is best described by a linear model, than the residual plot will

Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely To be . . .

A plot of the residuals versus the fitted values for record-breaking times of female marathon runners for the years 1998 - 2003 is: Based on this residuals plot, does it seem reasonable to use linear regression for this model? Explain.

Residuals are . . .

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?

On the axes below, sketch a scatterplot described: a. a strong negative association b. a strong association but $r$ is near 0 c. a weak but positive association

A consumer group collected information on HDTVs . They created a linear model to estimate the Cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the Slope of the line of best fit?

The correlation coefficient between the hours that a person is awake during a 24-hour period and The hours that same person is asleep during a 24-hour period is most likely to be

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. -Describe why performing linear regression with these data is not a good decision.

All but one of these statements contain a mistake. Which could be true?

Exploring and Understanding Data

Gathering Data

Randomness and Probability

From the Data at Hand to the World at Large

Accessing Associations Between Variables

Inference When Variables Are Related

Regression, Associations, and Predictive Modeling

Filters

Exam 2: Exploring Relationships Between Variables

If a data set has a relationship that is best described by a linear model, than the residual plot will

Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely To be . . .

A plot of the residuals versus the fitted values for record-breaking times of female marathon runners for the years 1998 - 2003 is: Based on this residuals plot, does it seem reasonable to use linear regression for this model? Explain.

Residuals are . . .

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?

On the axes below, sketch a scatterplot described: a. a strong negative association b. a strong association but rrr is near 0 c. a weak but positive association

A consumer group collected information on HDTVs . They created a linear model to estimate the Cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the Slope of the line of best fit?

The correlation coefficient between the hours that a person is awake during a 24-hour period and The hours that same person is asleep during a 24-hour period is most likely to be

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. -Describe why performing linear regression with these data is not a good decision.

All but one of these statements contain a mistake. Which could be true?

Exploring and Understanding Data

Gathering Data

Randomness and Probability

From the Data at Hand to the World at Large

Accessing Associations Between Variables

Inference When Variables Are Related

Regression, Associations, and Predictive Modeling

Filters

On the axes below, sketch a scatterplot described: a. a strong negative association b. a strong association but $r$ is near 0 c. a weak but positive association