Question 1

Which of the following statements regarding the correlation coefficient is not true?

Accepted Answer

A)   The correlation coefficient has values that range from -1.0 to 1.0 inclusive.
B)   A correlation coefficient value of 0.00 indicates that two variables have no linear correlation at all.
C)   The correlation coefficient measures the strength of the linear relationship between two numerical variables.
D)   All of these are true statements. D

Question 2

Based on the scatterplots below, what is the better predictor for head circumference--height or shoulder width?
 Explain how you made your decision.

Accepted Answer

Shoulder width; shoulder width has a stronger relationship with head circumference as shown by the scatterplot where points are less scattered in the vertical direction.

Question 3

Use the following information to answer the question. The following linear regression model can be used to predict ticketsales at a popular water park. $$\text { Ticket sales per hour } = - 631.25 + 11.25 \left( \text { current temperature in } { } ^ { \circ } \mathrm { F } \right)$$
-What is the predicted number of tickets sold per hour if the temperature is 79°F? Round to the nearest whole ticket.

Accepted Answer

A)   About 257 tickets
B)   About 310 tickets
C)   About 250 tickets
D)   About 258 tickets  D

Question 4

The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below. $$\begin{array} { | l | l | } 
\hline \text { Minutes } & \text { Calories } \
\hline 30 & 200 \
\hline 80 & 500 \
\hline 60 & 425 \
\hline 40 & 250 \
\hline 55 & 450 \
\hline
\end{array}$$

Accepted Answer

A)   -0.30
B)   0.99
C)   0.30
D)   -0.99

Question 5

The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars.  The relationship between "car length" and "car weight" can be described as

Accepted Answer

A)   A weak negative relationship
B)   A strong positive linear relationship
C)   A moderate positive linear relationship
D)   A strong negative linear relationship

Question 6

Use the following information to answer the question. The following linear regression model can be used to predict ticket
sales at a popular water park. Ticket sales per hour $= - 631.25 + 11.25 \left( \right.$ current temperature in ${ } ^ { \circ } \mathrm { F }$ )
-In the NBA, the correlation between "steals per game" and "blocked shots per game" is found to be 0.8045. Choose the statement that is true about the coefficient of determination.

Accepted Answer

A)   The coefficient of determination states that about 64.72% of the variation in blocked shots per game is explained by steals per game.
B)   The coefficient of determination, r2, is equal to approximately 0.6472.
C)   When given as a percent, the coefficient of determination is always between 0 and 100%.
D)   All of these are true statements.

Question 7

The following regression equation was found to model commute distance (in miles) andnumber of minor accidents per year for a group of adults. Minor accidents per year=1.204+0.024(commute distance) Identify the independent variable and the dependent variable.

Accepted Answer

The answer of The following regression equation was found to...

Question 8

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

Accepted Answer

A)   Negative
B)   Positive
C)   Near Zero

Question 9

The data in the table represent the amount of raw material (in tons) put into an injection moldingmachine each day (x), and the amount of scrap plastic (in tons) that is collected from the machineevery fourweeks (y).Also shown below are the outputs from two different statistical technologies(TI-83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association.Report the equation for predicting scrap from raw material using words such as scrap, notxandy.State the slope and intercept of the prediction equation. Round all calculations to the nearesthundredth
$\begin{array}{|c|c|}
\hline x & y \
\hline 2.71 & 3.61 \
\hline 2.33 & 2.80 \
\hline 2.33 & 2.77 \
\hline 2.21 & 2.34 \
\hline 2.11 & 2.15 \
\hline 2.08 & 2.06 \
\hline 1.98 & 2.02 \
\hline 1.95 & 1.95 \
\hline 1.84 & 1.73 \
\hline 1.84 & 1.68 \
\hline
\end{array}$

$\begin{array}{l}
\text { LinReg }\
y=a+b x \
a=-2.376991175 \
b=2.192699333 \
r^{2}=.9806834986 \
r=.9902946524
\end{array}$

$\begin{array}{|l|r|}
\hline & \text { Coefficients } \
\hline \text { Intercept } & -2.376991175 \
\hline \text { X Variable 1 } & 2.192699333 \
\hline
\end{array}$

Accepted Answer

A)   scrap  =−2.38+2.19= - 2.38 + 2.19=−2.38+2.19  (raw material) ; slope  =2.19= 2.19=2.19  and the intercept is  −2.38- 2.38−2.38 .
B)   scrap  =2.19−2.38= 2.19 - 2.38=2.19−2.38  (raw material) ; slope  =−2.38= - 2.38=−2.38  and the intercept is  2.192.192.19 .
C)   scrap  =2.19−2.38= 2.19 - 2.38=2.19−2.38  (raw material) ; slope  =2.19= 2.19=2.19  and the intercept is  −2.38- 2.38−2.38 .
D)   scrap  =−2.38+2.19= - 2.38 + 2.19=−2.38+2.19  (raw material) ; slope  =−2.38= - 2.38=−2.38  and the intercept is  2.192.192.19 .

Question 10

The scatterplot below shows the number of alcoholic drinks consumed and memory testresults for some college students. Is there an association?
 If so, describe the pattern. Be sureto comment on trend, shape, and the strength of the association.

Accepted Answer

The answer of The scatterplot below shows the number of...

Question 11

The scatterplot below shows the ice cream sales and daily high temperatures for a threeweek period of time during the summer. Does there appear to be an association betweenthese two variables?
 If so, describe the pattern. Be sure to comment on trend, shape, and thestrength of the association.

Accepted Answer

The answer of The scatterplot below shows the ice cream...

Question 12

The following regression equation was found to model commute distance (in miles) andnumber of minor accidents per year for a group of adults.  Minor accidents per year=1.204+0.024(commute distance)  What is the intercept?
 What is the interpretation of the intercept in this context?
 Does itmake sense to interpret the intercept in this context?

Accepted Answer

The answer of The following regression equation was found to...

Question 13

It is determined that a positive linear association exists between age (for children between the agesof 3 and 9 years) and attention span (measured in minutes). The scatterplot below shows theassociation. The prediction equation is also given. A college instructor uses the model to predict theattention span of the students in her class who have an average age of 29. Choose the best statementto summarize why this is not an appropriate use for the model.

attention span $= 4.68 + 3.40$ (age)

Accepted Answer

A)   This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The college instructor is extrapolating.
B)   This is an inappropriate use of the model because age does not cause attention span toIncrease. Correlation does not mean causation.
C)   This is an inappropriate use of the model because a 29-year-old person would be an outlierIn this context.

Question 14

Use the following information to answer the question. The following linear regression model can be used to predict ticketsales at a popular water park.

Ticket sales per hour=-631.25+11.25(current temperature in °F)
-Choose the statement that best states the meaning of the slope in this context.

Accepted Answer

A)  The slope tells us that if ticket sales are decreasing there must have been a drop intemperature.
B)  The slope tells us that high temperatures are causing more people to buy tickets to the waterpark.
C)  The slope tells us that a one degree increase in temperature is associated with an averageincrease in ticket sales of 11.25 tickets.
D)  None of these

Question 15

A horticulturist conducted an experiment on 140 thirty-six inch plant boxes to see if the amount ofplant food given to the plant boxes was associated with the number of habanera peppers harvestedfrom the plants. The average amount of plant food given was 17.8 milliliters with a standarddeviation of 0.7 milliliters. The average number of habanera peppers harvested was 6.5 with astandard deviation of 1.5. The correlation coefficient was 0.8123. Use the information to calculatethe slope of the linear model that predicts the number of habanera peppers harvested from theamount of plant food given. Show your work and round to the nearest hundredth.   
A) $1.74$ 
B) The slope cannot be determined without the actual data. 
C) $0.38$ 
D) $- 1.50$

Accepted Answer

The answer of A horticulturist conducted an experiment on 140...

Question 16

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

Accepted Answer

A)   Positive
B)   Near Zero
C)   Negative

Question 17

Suppose that environmentalists monitor algae levels in a river and determine that there is alinear association between local rainfall and algae levels. The determine that the best fittinglinear model to predict algae cell counts per milliliter from rainfall in inches is:
  Algae cell count=229.32+79.81(Rainfall in inches) withr2=0.604  How will a rainfall that is 3 inches above average affect the algae cell count?

Accepted Answer

The answer of Suppose that environmentalists monitor algae levels in...

Question 18

Doctors hypothesize that smoking cigarettes inflames the bronchial tubes and so makes it harder tobreathe. To test this they measured the lung capacity (in liters) and the number of cigarettessmoked in a typical day for a sample of adults. Is the scatterplot below consistent with theresearcher's hypothesis?

Accepted Answer

A)   No, it contradicts this hypothesis.
B)   There is no evidence in support or contradiction of the hypothesis.
C)   Yes, it is consistent.

Question 19

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expendituresfor eight families. City size is in thousands and expenditures is in hundreds of dollars. $$\begin{array} { | c | c | }  \hline \begin{array} { c }  \text { City Size } \ \text { (in } \ \text { thousands) } \end{array} & \begin{array} { c }  \text { Grocery } \ \text { Expenditures } \ \text { (in hundreds } \ \text { of dollars) } \end{array} \ \hline 30 & 65 \ \hline 50 & 77 \ \hline 75 & 79 \ \hline 100 & 80 \ \hline 150 & 82 \ \hline 200 & 90 \ \hline 175 & 84 \ \hline 120 & 81 \ \hline \end{array}$$
-State the slope and intercept of the regression line and explain each in context. Be sure toexplain whether the intercept has a practical meaning in this context.

Accepted Answer

The answer of Use the data provided in the table...

Question 20

Use the following information to answer the question. A scatterplot of data from a large sample of adult women shows that height in inches and weight in pounds have a linear association. Shown below are the outputs from two different statistical technologies (TI-83/84 Calculator and Excel).
T-Test
$
\begin{array}{l}
y=a+b x \
a=-23.86734694 \
b=2.581632653 \
r^{2}=.7648162309 \
r=.8745377241
\end{array}
$
$\begin{array}{|l|r|}
\hline &{\text { Coefficients }} \
\hline \text { Intercept } & -23.86734694 \
\hline \text { X Variable 1 } & 2.581632653 \
\hline
\end{array}$
-Report the equation for predicting weight in pounds from height in inches using wordssuch as weight, notxandy.

Accepted Answer

The answer of Use the following information to answer the...

Exam 4: Regression Analysis: Exploring Associations Between Variables

Which of the following statements regarding the correlation coefficient is not true?

Based on the scatterplots below, what is the better predictor for head circumference--height or shoulder width? Explain how you made your decision.

The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars. The relationship between "car length" and "car weight" can be described as

The following regression equation was found to model commute distance (in miles) andnumber of minor accidents per year for a group of adults. Minor accidents per year=1.204+0.024(commute distance) Identify the independent variable and the dependent variable.

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

The scatterplot below shows the number of alcoholic drinks consumed and memory testresults for some college students. Is there an association? If so, describe the pattern. Be sureto comment on trend, shape, and the strength of the association.

The scatterplot below shows the ice cream sales and daily high temperatures for a threeweek period of time during the summer. Does there appear to be an association betweenthese two variables? If so, describe the pattern. Be sure to comment on trend, shape, and thestrength of the association.

Use the following information to answer the question. The following linear regression model can be used to predict ticketsales at a popular water park. Ticket sales per hour=-631.25+11.25(current temperature in °F) -Choose the statement that best states the meaning of the slope in this context.

The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?