Question 1

What key things should you look for when examining the potential linear association between two variables?

Accepted Answer

A)  A noticeable overall linear shape on the scatterplot. 
B)  The vertical spread of the points on the scatterplot which indicate the strength of an association. 
C)  A noticeable positive or negative trend on the scatterplot. 
D)  All of these. 
A)  A noticeable overall linear shape on the scatterplot. 
B)  The vertical spread of the points on the scatterplot which indicate the strength of an association. 
C)  A noticeable positive or negative trend on the scatterplot. 
D)  All of these.

Question 2

The data in the table represent the amount of pressure (psi) exerted by a stamping machine (x), and the amount of scrap brass shavings (in pounds) that are collected from the machine each hour (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 brass shavings using words such as scrap, not x and y. State the slope and
Intercept of the prediction equation. Round all calculations to the nearest thousandth. $\begin{array}{|c|r|}
\hline x & y \
\hline 2.00 & 2.30 \
\hline 7.80 & 15.14 \
\hline 14.51 & 28.65 \
\hline 2.80 & 4.15 \
\hline 4.01 & 6.35 \
\hline 6.21 & 10.52 \
\hline 11.84 & 24.05 \
\hline 5.11 & 8.75 \
\hline 11.67 & 22.22 \
\hline 8.70 & 17.02 \
\hline
\end{array}$

T-Test
$\begin{array} { l } 
y = a + b x \
a = - 2.018775528 \
b = 2.134464237 \
r ^ { 2 } = .996074796 \
r = .998035467
\end{array}$

$\begin{array}{|l|r|}
\hline & \multicolumn{1}{|c|}{\text { Coefficients }} \
\hline \text { Intercept } & -2.018775528 \
\hline \text { X Variable 1 } & 2.134464237 \
\hline
\end{array}$

Accepted Answer

A)  scrap $= - 2.019 + 2.134$ (pressure); slope $= - 2.019$ and the intercept is $2.134$. 
B)  scrap $= 2.134 - 2.019$ (pressure); slope $= - 2.019$ and the intercept is $2.134$. 
C)  scrap $= - 2.019 + 2.134$ (pressure); slope $= 2.134$ and the intercept is $- 2.019$. 
D)  scrap $= 2.134 - 2.019$ (pressure); slope $= 2.134$ and the intercept is $- 2.019$. 
A)  scrap $= - 2.019 + 2.134$ (pressure); slope $= - 2.019$ and the intercept is $2.134$. 
B)  scrap $= 2.134 - 2.019$ (pressure); slope $= - 2.019$ and the intercept is $2.134$. 
C)  scrap $= - 2.019 + 2.134$ (pressure); slope $= 2.134$ and the intercept is $- 2.019$. 
D)  scrap $= 2.134 - 2.019$ (pressure); slope $= 2.134$ and the intercept is $- 2.019$.

Question 3

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

Accepted Answer

A)  The correlation coefficient measures the strength of the linear relationship between two numerical variables. 
B)  A value of 0.00 indicates that two variables are perfectly linearly correlated. 
C)  The correlation coefficient has values that range from -1.0 to 1.0 inclusive. 
D)  All of these are true statements. 
A)  The correlation coefficient measures the strength of the linear relationship between two numerical variables. 
B)  A value of 0.00 indicates that two variables are perfectly linearly correlated. 
C)  The correlation coefficient has values that range from -1.0 to 1.0 inclusive. 
D)  All of these are true statements.

Question 4

$$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { City Size } \
\text { (in } \
\text { thousands) }
\end{array} & \begin{array} { c } 
\text { Grocery } \
\text { Expenditures } \
\text { (in hundreds } \
\text { of dollars) }
\end{array} \
\hline 30 & 65 \
\hline 50 & 77 \
\hline 75 & 79 \
\hline 100 & 80 \
\hline 150 & 82 \
\hline 200 & 90 \
\hline 175 & 84 \
\hline 120 & 81 \
\hline
\end{array}$$
-Using the data from the table, sketch a scatterplot (by hand or with the aid of technology)of the data. Describe any association that you see. Would it be appropriate to fit a linearmodel to this data?

Accepted Answer

The scatterplot shows a positi

Question 5

Choose the scatterplot that matches the given correlation coefficient.
-$$r = - 0.6542$$

Accepted Answer

A) 
  
B) 
  
C) 
  
A) 
  
B) 
  
C)

Question 6

Choose the scatterplot that matches the given correlation coefficient.
-$$r = - 0.3526$$

Accepted Answer

A) 
  
B) 
  
C) 
  
A) 
  
B) 
  
C)

Question 7

Suppose that runner height (in inches) and finish time in a 5k (in seconds) have a linearassociation as evidenced by a scatterplot showing a roughly linear pattern, explain thepurpose of finding the equation for the regression line that will relate runner height andfinish time. What are the limitations of the regression line?
 Explain the meaning of theslope and intercept of such a model?

Accepted Answer

The purpose of the regression line is to

Question 8

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 co relationCoefficient from the answer choices below.

$\begin{array}{|l|l|}
\hline \text { Minutes } & \text { Calories } \
\hline 30 & 250 \
\hline 75 & 500 \
\hline 65 & 425 \
\hline 40 & 300 \
\hline 55 & 375 \
\hline
\end{array}$

Accepted Answer

A)  $- 0.99$ 
B)  $- 0.20$ 
C)  $0.20$ 
D)  $0.99$ 
A)  $- 0.99$ 
B)  $- 0.20$ 
C)  $0.20$ 
D)  $0.99$

Question 9

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. $$\begin{array} { | c | c | }  \hline \begin{array} { c }  \text { City Size } \ \text { (in } \ \text { thousands) } \end{array} & \begin{array} { c }  \text { Grocery } \ \text { Expenditures } \ \text { (in hundreds } \ \text { of dollars) } \end{array} \ \hline 30 & 65 \ \hline 50 & 77 \ \hline 75 & 79 \ \hline 100 & 80 \ \hline 150 & 82 \ \hline 200 & 90 \ \hline 175 & 84 \ \hline 120 & 81 \ \hline \end{array}$$
-Suppose each of these families is given a grocery credit of $100, therefore reducingexpenditures in the table by one unit (since this variable was recorded in hundreds ofdollars). Estimate the new correlation with city size. What happens to the correlation whena constant is added (in this case-100 dollars is added to each number)?
 Explain yourreasoning.

Accepted Answer

The estimate for r should not

Question 10

A concert ticket agent is going to investigate whether an increase in money spent on radioadvertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, theresponse variable-------------------- isand the explanatory variable is--------------------

Accepted Answer

A)  Slope; intercept 
B)  Amount of radio advertisement money spent; concert ticket sales 
C)  Concert ticket sales; amount of radio advertisement money spent 
D)  None of these 
A)  Slope; intercept 
B)  Amount of radio advertisement money spent; concert ticket sales 
C)  Concert ticket sales; amount of radio advertisement money spent 
D)  None of these

Question 11

The scatterplot below shows the number of tackles received and the number of concussionsreceived for a team of football players for the most recent season. Choose the statement that bestdescribes the trend.

Accepted Answer

A)  Teams that receive a greater number of tackles tend to have a higher number of concussions. 
B)  There is no association between the number of tackles a team receives and the number of concussions. 
C)  Teams that receive a greater number of tackles tend to receive a lower number of concussions. 
A)  Teams that receive a greater number of tackles tend to have a higher number of concussions. 
B)  There is no association between the number of tackles a team receives and the number of concussions. 
C)  Teams that receive a greater number of tackles tend to receive a lower number of concussions.

Question 12

The figures below show the relationship between salary and personal lunch expenses onweek days for a group of business men. Comment on the difference in graphs and in thecoefficient of determination between the graph that includes a data point of someone whoreported earnings of $21,000 per year and weekly personal lunch expenses of $100 perweek (second graph) and the graph that did not include this data point (first graph).

Accepted Answer

The coefficient of determinati

Question 13

A horticulturist conducted an experiment on 110 thirty-six inch plant boxes to see if the amount ofplant food given to the plant boxes was associated with the number of tomatoes harvested from theplants. The average amount of plant food given was 27.8 milliliters with a standard deviation of 2.1milliliters. The average number of tomatoes harvested was 7.5 with a standard deviation of 1.5. Thecorrelation coefficient was 0.7691. Use the information to calculate the slope of the linear model thatpredicts the number of tomatoes harvested from the amount of plant food given. Show your workand round to the nearest hundredth.

Accepted Answer

A)  1.08 
B)  0.55 
C)  -7.50 
D)  The slope cannot be determined without the actual data. 
A)  1.08 
B)  0.55 
C)  -7.50 
D)  The slope cannot be determined without the actual data.

Question 14

It is determined that a positive linear association exists between amount of a new smokingcessation drug taken (in milliliters) and weight gain in women (in pounds). The scatterplot belowshows the association. The prediction equation is also given. A pharmacy technician uses the modelto predict the potential weight gain for a man who takes the recommended dosage. Choose the beststatement to summarize why this is not an appropriate use for the model.

Accepted Answer

A)  This is an inappropriate use of the model because taking the smoking cessation drug does not cause weight gain. Correlation does not mean causation. 
B)  This is an inappropriate use of the model because a man would be an outlier in this context. 
C)  This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The Pharmecy Technician is extrapolating. 
A)  This is an inappropriate use of the model because taking the smoking cessation drug does not cause weight gain. Correlation does not mean causation. 
B)  This is an inappropriate use of the model because a man would be an outlier in this context. 
C)  This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The Pharmecy Technician is extrapolating.

Question 15

Choose the scatterplot that matches the given correlation coefficient.
-$r = 0.8787$

Accepted Answer

A) 
  
B) 
  
C) 
  
A) 
  
B) 
  
C)

Question 16

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is-------------------- and the response variable is--------------------

Accepted Answer

A)  Number of pets; number of fleas spotted in a period of time 
B)  Slope; intercept 
C)  Number of fleas spotted in a period of time; number of pets 
D)  None of these 
A)  Number of pets; number of fleas spotted in a period of time 
B)  Slope; intercept 
C)  Number of fleas spotted in a period of time; number of pets 
D)  None of these

Question 17

Suppose it has been established that "annual income" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation:
Annual Income $= \$ 23,400 + \$ 7200$ (Years of College $)$. In this model, "Annual Income" is the $\frac{?}{}$   variable, and "Years of College" is  the$\frac{?}{}$   variable,  The two  variables have a  $\frac{?}{}$ linear relationship.

Accepted Answer

A)  Independent; Dependent; Positive 
B)  Independent; Dependent; Negative 
C)  Dependent; Independent; Negative 
D)  Dependent; Independent; Positive 
A)  Independent; Dependent; Positive 
B)  Independent; Dependent; Negative 
C)  Dependent; Independent; Negative 
D)  Dependent; Independent; Positive

Question 18

The following calculator screenshots show the scatterplot and the correlation coefficient between the number of days absent and the final grade for a sample of college students in a general education statistics course at a large community college.   The relationship between "days absent" and "final grade" can be described as

Accepted Answer

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

What key things should you look for when examining the potential linear association between two variables?

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

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.6542$

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.3526$

A concert ticket agent is going to investigate whether an increase in money spent on radioadvertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, theresponse variable_{--------------------} isand the explanatory variable is_{--------------------}

The scatterplot below shows the number of tackles received and the number of concussionsreceived for a team of football players for the most recent season. Choose the statement that bestdescribes the trend.

Choose the scatterplot that matches the given correlation coefficient. - $r = 0.8787$

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is_{--------------------} and the response variable is_{--------------------}

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Modeling Variation With Probability

Modeling Random Events: the Normal and Binomial Models

Survey Sampling and Inference

Hypothesis Testing for Population Proportions

Inferring Population Means

Associations Between Categorical Variables

Multiple Comparisons and Analysis of Variance

Experimental Design: Controlling Variation

Inference Without Normality

Inference for Regression

Filters

Exam 4: Regression Analysis: Exploring Associations Between Variables

What key things should you look for when examining the potential linear association between two variables?

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

Choose the scatterplot that matches the given correlation coefficient. - r=−0.6542r = - 0.6542r=−0.6542

Choose the scatterplot that matches the given correlation coefficient. - r=−0.3526r = - 0.3526r=−0.3526

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 co relationCoefficient from the answer choices below. Minutes Calories 30 250 75 500 65 425 40 300 55 375

A concert ticket agent is going to investigate whether an increase in money spent on radioadvertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, theresponse variable-------------------- isand the explanatory variable is--------------------

The scatterplot below shows the number of tackles received and the number of concussionsreceived for a team of football players for the most recent season. Choose the statement that bestdescribes the trend.

Choose the scatterplot that matches the given correlation coefficient. - r=0.8787r = 0.8787r=0.8787

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is-------------------- and the response variable is--------------------

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Modeling Variation With Probability

Modeling Random Events: the Normal and Binomial Models

Survey Sampling and Inference

Hypothesis Testing for Population Proportions

Inferring Population Means

Associations Between Categorical Variables

Multiple Comparisons and Analysis of Variance

Experimental Design: Controlling Variation

Inference Without Normality

Inference for Regression

Filters

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.6542$

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.3526$

A concert ticket agent is going to investigate whether an increase in money spent on radioadvertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, theresponse variable_{--------------------} isand the explanatory variable is_{--------------------}

Choose the scatterplot that matches the given correlation coefficient. - $r = 0.8787$

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is_{--------------------} and the response variable is_{--------------------}