Question 1

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

Accepted Answer

A)  A residual plot can highlight the existence of a nonconstant standard deviation even when it is hard to see in the original scatterplot. 
B)  A QQ plot can help you determine whether the constant standard deviation condition holds. 
C)  A fan shape in a residual plot indicates that the constant standard deviation condition does not hold. 
D)  A constant standard deviation means that the vertical spread of the y-values about the line is the same across the entire line. 
A)  A residual plot can highlight the existence of a nonconstant standard deviation even when it is hard to see in the original scatterplot. 
B)  A QQ plot can help you determine whether the constant standard deviation condition holds. 
C)  A fan shape in a residual plot indicates that the constant standard deviation condition does not hold. 
D)  A constant standard deviation means that the vertical spread of the y-values about the line is the same across the entire line. B

Question 2

Which of the following statements is true about prediction intervals?

Accepted Answer

A)  The width of the prediction interval is affected by the size of the standard deviation of the population distribution. 
B)  A prediction interval is concerned with predicting values for individuals. 
C)  Prediction intervals are wider than confidence intervals because there is more uncertainty in predicting an individual's value. 
D)  All of these statements are true. 
A)  The width of the prediction interval is affected by the size of the standard deviation of the population distribution. 
B)  A prediction interval is concerned with predicting values for individuals. 
C)  Prediction intervals are wider than confidence intervals because there is more uncertainty in predicting an individual's value. 
D)  All of these statements are true. D

Question 3

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

Accepted Answer

A)  A constant standard deviation means that the vertical spread of the y-values about the line is the same across the entire line. 
B)  A residual plot can highlight the existence of a nonconstant standard deviation even when it is hard to see in the original scatterplot. 
C)  A fan shape in a residual plot indicates that the constant standard deviation condition does not hold. 
D)  All of these are true about the constant standard condition. 
A)  A constant standard deviation means that the vertical spread of the y-values about the line is the same across the entire line. 
B)  A residual plot can highlight the existence of a nonconstant standard deviation even when it is hard to see in the original scatterplot. 
C)  A fan shape in a residual plot indicates that the constant standard deviation condition does not hold. 
D)  All of these are true about the constant standard condition. D

Question 4

Use the following information to answer the question. A random sample of 30 married couples were asked to report the
height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression
analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model
are satisfied. $$\begin{array} { | l | l | } 
\hline  { \text { Regression Analysis: Spouse versus Parent } } \
\hline \text { The regression equation is } & \
\text { spouse } = 48.40 + 0.25 \text { parent } & \
\text { Predictor: Constant } & \text { Predictor: Parent } \
\text { Parameter Estimate: } 48.398 & \text { Parameter Estimate: } 0.247 \
\text { Standard Error: } 39.695 & \text { Standard Error: } 0.566 \
\text { T-statistic: } 1.219 & \text { T-statistic: } 0.437 \
\text { p-value: } 0.277 & \text { p-value: } 0.680 \
\hline \mathrm { S } = 7.794899045 \quad \mathrm { R } - \mathrm { sq } = 0.036858791 \quad \mathrm { r } = 0.1919864344 \
\hline
\end{array}$$
-What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context.

Accepted Answer

A)  The slope is 0.25. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample. 
B)  The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 48.40 inches taller, in the sample. 
C)  The slope is 0.25. On average, for each 0.25 inches taller a parent is, the spouse is about 1 inch taller, in the sample. 
D)  The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample. 
A)  The slope is 0.25. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample. 
B)  The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 48.40 inches taller, in the sample. 
C)  The slope is 0.25. On average, for each 0.25 inches taller a parent is, the spouse is about 1 inch taller, in the sample. 
D)  The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample.

Question 5

State the two conditions that must be satisfied, without exception, to make inferences using a linear model.

Accepted Answer

(1) the linearity condition an

Question 6

Use the following information to answer the question. Below is the scatterplot showing the association between raw material (in tons) put into an injection molding machine each day $( x )$, and the amount of scrap plastic (in tons) that is collected from the machine every 4 weeks $( y )$. The residual plot of the data is also shown along with a QQ plot of the residuals.

-Choose the statement that is true about the estimators for slope and intercept of a regression line when the conditions of the linear model hold.

Accepted Answer

A)  The sampling distributions of the estimators follow the chi-square model. 
B)  The standard errors for the estimators must come from a population that is Normally distributed. 
C)  The estimators for the slope and intercept of a regression line are unbiased. 
D)  None of these 
A)  The sampling distributions of the estimators follow the chi-square model. 
B)  The standard errors for the estimators must come from a population that is Normally distributed. 
C)  The estimators for the slope and intercept of a regression line are unbiased. 
D)  None of these

Question 7

The regression output below is the result of testing whether there is an association between the number of practice test problems a student completed and the number of questions answered
Correctly on the test. Assume that the conditions of the linear regression model are satisfied. What
Is the 95% confidence interval for the intercept (rounded to the nearest hundredth)? Does this
Interval support the theory that the intercept is zero? Choose the statement that summarizes your
Answer in context. $\begin{array}{|l|l|l|l|l|}
\hline & \text { Coefficients } & \begin{array}{l}
\text { Standard } \
\text { Error }
\end{array} & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -2.12319885 & 2.3432 & -8.14673883 & 3.90034114 \
\hline \text { Slope } & 1.108789625 & 0.0977 & 0.85765303 & 1.359926221 \
\hline
\end{array}$

Accepted Answer

A)  $( 0.86,1.36 )$. This interval does not support the theory that the intercept could be zero. In this context the intercept is greater than zero so a student could expect to get a positive score on the test even if they did none of the practice problems. 
B)  $( - 8.15,3.90 )$. This interval does not support the theory that the intercept could be zero. In this context this would mean that for approximately every two practice problems completed, the student could expect to get approximately one test question correct. 
C)  $( - 8.15,3.90 )$. This interval supports the theory that the intercept could be zero. In this context this would mean that a student who completed zero practice test problems could reasonably expect to get a zero on the test. 
D)  None of these 
A)  $( 0.86,1.36 )$. This interval does not support the theory that the intercept could be zero. In this context the intercept is greater than zero so a student could expect to get a positive score on the test even if they did none of the practice problems. 
B)  $( - 8.15,3.90 )$. This interval does not support the theory that the intercept could be zero. In this context this would mean that for approximately every two practice problems completed, the student could expect to get approximately one test question correct. 
C)  $( - 8.15,3.90 )$. This interval supports the theory that the intercept could be zero. In this context this would mean that a student who completed zero practice test problems could reasonably expect to get a zero on the test. 
D)  None of these

Question 8

Use the following information to answer the question. Below is the scatterplot showing the association between the number of workers on an assembly team (x), and the number of parts assembled in an 8-hour shift (y). The residual plot of the data is also shown along with a QQ plot of the residuals.  
-Use the plot(s) above to explain whether the condition for constant standard deviation is satisfied.

Accepted Answer

The residual plot does not hav

Question 9

Use the following information to answer the question. The pulse rate of a random sample of 30 second graders was recorded before and after a fifteen minute recess. The output of a regression analysis for predicting pulse rate after recess from pulse rate before recess is shown. Assume that the conditions of the linear regression model are satisfied. $$\begin{array} { | l | l | }  \hline{ \text { Regression Analysis:
 Pulse before recess versus Pulse after recess } } \ \hline \text { The regression equation is } & \ \text { pulse before } = 14.62 + 0.92 \text { pulse after } & \ \text { Predictor:
 Constant } & \text { Predictor:
 Pulse before } \ \text { Parameter Estimate:
 } 14.6190 & \text { Parameter Estimate:
 } 0.9167 \ \text { Standard Error:
 } 8.536 & \text { Standard Error:
 } 0.111 \ \text { T-statistic:
 } 1.713 & \text { T-statistic:
 8.26 } \ \text { p-value:
 } 0.147 & \text { p-value:
 } 0.000 \ \hline S = 7.794899045 \quad \text { R-sq=0.036858791 } & \text { r=0.1919864344 } \ \hline \end{array}$$
-If the intercept was 0 and the slope was 1, explain how the linear model would be interpreted in context.

Accepted Answer

It would mean that o

Question 10

The regression output below is the result of testing whether there is an association between the number of hours of sleep a student had the night before an exam and the number of questions
Answered correctly on the exam. Assume that the conditions of the linear regression model are
Satisfied. What is the 95% confidence interval for the intercept (rounded to the nearest hundredth)?
Does this interval support the theory that the intercept is zero? Choose the statement that
Summarizes your answer in context. $\begin{array}{|l|l|l|l|l|}
\hline & \text { Coefficients } & \begin{array}{l}
\text { Standard } \
\text { Error }
\end{array} & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -0.25 & 1.85713484 & -4.64144652 & 4.14144652 \
\hline \text { Slope } & 0.087621024 & 0.023022636 & 0.033181139 & 0.142060908 \
\hline
\end{array}$

Accepted Answer

A)  $( - 4.64,4.14 )$. This interval supports the theory that the intercept could be zero. In this context this would mean that a student who had zero hours of sleep could reasonably expect to get a zero on the test. 
B)  $( - 4.64,4.14 )$. This interval does not support the theory that the intercept could be zero. In this context this would mean that for approximately every $0.08$ hours of sleep, the student could expect to get approximately one test question correct. 
C)  $( 0.03,0.14 )$. This interval does not support the theory that the intercept could be zero. In this context the intercept is greater than zero so a student could expect to get a positive score on the test even if they did not get any hours of sleep. 
D)  None of these 
A)  $( - 4.64,4.14 )$. This interval supports the theory that the intercept could be zero. In this context this would mean that a student who had zero hours of sleep could reasonably expect to get a zero on the test. 
B)  $( - 4.64,4.14 )$. This interval does not support the theory that the intercept could be zero. In this context this would mean that for approximately every $0.08$ hours of sleep, the student could expect to get approximately one test question correct. 
C)  $( 0.03,0.14 )$. This interval does not support the theory that the intercept could be zero. In this context the intercept is greater than zero so a student could expect to get a positive score on the test even if they did not get any hours of sleep. 
D)  None of these

Question 11

Suppose that you were presented with data showing the association between days absent from class and final class average. Which of the following residual plots below suggests that the
Association between number of days absent from class and final class average is linear?

Accepted Answer

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

Question 12

Use the following information to answer the question. A statistics professor is interested in learning whether there is a
positive association between number of posts by online students on a message board and the final class average in an online
statistics course. The computer output below shows the results from a regression model in which the final class average was
predicted by the number of message board posts. Assume that the conditions of the linear regression model are satisfied. $$\begin{array} { | l l | } 
\hline { \text { LinRegTTest for } y = a + b x } \
\hline \beta > 0 & a = 69.7104476 \
t = 3.707824045 & b = .8144278607 \
p = 0.0024306618 & s = 5.14275481 \
d f = 119 & r = .7774060152 \
\hline
\end{array}$$
-Choose the correct observed value of the test statistic and the p-value. Round to the nearest thousandth.

Accepted Answer

A)  $t = 0.777 , p = 0.002$ 
B)  $t = 3.708 , p = 0.002$ 
C)  $t = 0.002 , p = 3.707$ 
D)  $t = 3.708 , p = 0.005$ 
A)  $t = 0.777 , p = 0.002$ 
B)  $t = 3.708 , p = 0.002$ 
C)  $t = 0.002 , p = 3.707$ 
D)  $t = 3.708 , p = 0.005$

Question 13

Use the following information to answer the question. A high school boys track and field coach performs a regression to predict the vault height (in feet) of a pole vault from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Regression Analysis: Training versus vault height
The regression equation is vault height $ =12.75+0.015 $ training minutes 
Predicted Values:
$\begin{array}{|l|l|l|l|l|}
\hline \mathrm{X} \text { value } & \text { Pred. Y } & \text { s.e. (Pred. y) } & \text { 95\% C.I. } & \text { 95\% P.I. } \
\hline 175 & 15.375 & 1.24113 & (12.275,18.475) & (10.875,19.875) \
\hline
\end{array}$
-Suppose the coach's top pole vaulter trained for 175 minutes the previous week. If this athlete participates in the pole vault event, what is the coach's expected jump height for this athlete?
 Can he be reasonably confident that this athlete will beat the previous season's record of 19.8 feet?
 Explain.

Accepted Answer

Expected pole vault height is

Question 14

Use the following information to answer the question. An engineer is interested in learning whether there is an association between temperature (°F) and the strength of an automotive plastic cup holder which is measured by finding the pounds per square inch (psi) it takes to break the cup holder. The computer output below shows the results from a regression model in which the breaking point in psi was predicted by the temperature. Assume that the conditions of the linear regression model are satisfied. $$\begin{array} { | l l | }  \hline { \text { LinRegTTest for } y = a + b x } \ \hline \beta > 0 & a = 10.06846186 \ t = 5.9838909 & b = .2252509467 \ p = 9.3423882 E - 4 & s = 2.595293293 \ d f = 119 & r = .9367346759 \ \hline \end{array}$$
-State the decision regarding the null hypothesis and the correct conclusion. State your conclusion using a significance level of 5%.

Accepted Answer

@#LAT-DLM& . There is enough evidence to

Question 15

Test the hypothesis that the slope is zero (significance level is 0.05), then state the correct decision regarding the null hypothesis and write a statement that correctly summarizes the conclusion in context.

Accepted Answer

Reject @#LAT-DLM&. There is enough evide

Question 16

Which of the following is not true about the coefficient of determination, $r ^ { 2 }$ ?

Accepted Answer

A)  In order to interpret $r ^ { 2 }$ the linearity condition of the linear regression model must be satisfied. 
B)  The coefficient of determination, $r ^ { 2 }$, is a statistic that will give some information about how well the data fits the model, but it should not be the only piece of information taken into consideration when determining how useful a linear model might be. 
C)  A hypothesis test should be conducted verify that $r ^ { 2 }$ is large enough to conclude a linear relationship exists. 
D)  The coefficient of determination, $r ^ { 2 }$, ranges from $0 \%$ to $100 \%$ and represents the amount of variability in the response variable $( y )$ explained by the regression line. 
A)  In order to interpret $r ^ { 2 }$ the linearity condition of the linear regression model must be satisfied. 
B)  The coefficient of determination, $r ^ { 2 }$, is a statistic that will give some information about how well the data fits the model, but it should not be the only piece of information taken into consideration when determining how useful a linear model might be. 
C)  A hypothesis test should be conducted verify that $r ^ { 2 }$ is large enough to conclude a linear relationship exists. 
D)  The coefficient of determination, $r ^ { 2 }$, ranges from $0 \%$ to $100 \%$ and represents the amount of variability in the response variable $( y )$ explained by the regression line.

Question 17

Explain what residuals are. Where do residuals come from?
 How are residuals calculated?
 Complete the table below by calculating the residuals for the following small data set. The linear model relating $x$ and $y$ is $y = 5 - 10 x$. $\begin{array}{|l|l|l|} \hline x & y & \text { Residual } \ \hline 11 & -100 & \ \hline 5 & -51 & \ \hline 7 & -63 & \ \hline 4 & -34 & \ \hline \end{array}$

Accepted Answer

The residual is the variation from the l

Question 18

Use the following information to answer the question. A high school boys track and field coach performs a regression to predict the vault height (in feet) of a pole vault from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Regression Analysis: Training versus vault height
The regression equation is vault height $ =12.75+0.015 $ training minutes
Predicted Values:
$\begin{array}{|l|l|l|l|l|}
\hline X \text { value } & \text { Pred. Y } & \text { s.e. (Pred. y) } & \text { 95\% C.I. } & \text { 95\% P.I. } \
\hline 175 & 15.375 & 1.24113 & (12.275,18.475) & (10.875,19.875) \
\hline
\end{array}$
-The coach wants to project what the jump height of his top pole vaulter will be who trained for 175 minutes the previous week. Should the coach use a confidence interval or a prediction interval?

Accepted Answer

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

Question 19

Which of the following is not true about residuals? If all the statements are true choose (d).

Accepted Answer

A)  The residuals can be determined by finding the difference between the actual observed value and the predicted dependent variable. 
B)  The residuals are the result of natural variation in the independent variable. 
C)  The residuals can be described as the excess, due to randomness, that doesn't fit on the line. 
D)  All of these are true. 
A)  The residuals can be determined by finding the difference between the actual observed value and the predicted dependent variable. 
B)  The residuals are the result of natural variation in the independent variable. 
C)  The residuals can be described as the excess, due to randomness, that doesn't fit on the line. 
D)  All of these are true.

Question 20

Use the following information to answer the question. A random sample of 30 married couples were asked to report the
height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression
analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model
are satisfied. $$\begin{array} { | l | l | } 
\hline { \text { Regression Analysis: Spouse versus Parent } } \
\hline \text { The regression equation is } & \
\text { spouse } = 48.40 + 0.25 \text { parent } & \
\text { Predictor: Constant } & \text { Predictor: Parent } \
\text { Parameter Estimate: } 48.398 & \text { Parameter Estimate: } 0.247 \
\text { Standard Error: } 39.695 & \text { Standard Error: } 0.566 \
\text { T-statistic: } 1.219 & \text { T-statistic: } 0.437 \
\text { p-value: } 0.277 & \text { p-value: } 0.680 \
\hline \text { S=7.794899045 } \quad \text { R-sq } = 0.036858791 \quad \mathrm { r } = 0.1919864344 \
\hline
\end{array}$$
-Test the hypothesis that the slope is zero (significance level is 0.05), then choose the correct decision regarding the null hypothesis and the statement that correctly summarizes the conclusion.

Accepted Answer

A)  Fail to reject $\mathrm { H } _ { 0 }$. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between parent height and spouse height. 
B)  Reject $\mathrm { H } _ { 0 }$. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between parent height and spouse height. 
C)  Reject $\mathrm { H } _ { 0 }$. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between parent height and spouse height. 
D)  Fail to reject $\mathrm { H } _ { 0 }$. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between parent height and spouse height. 
A)  Fail to reject $\mathrm { H } _ { 0 }$. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between parent height and spouse height. 
B)  Reject $\mathrm { H } _ { 0 }$. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between parent height and spouse height. 
C)  Reject $\mathrm { H } _ { 0 }$. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between parent height and spouse height. 
D)  Fail to reject $\mathrm { H } _ { 0 }$. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between parent height and spouse height.

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

Which of the following statements is true about prediction intervals?

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

State the two conditions that must be satisfied, without exception, to make inferences using a linear model.

Suppose that you were presented with data showing the association between days absent from class and final class average. Which of the following residual plots below suggests that the Association between number of days absent from class and final class average is linear?

Test the hypothesis that the slope is zero (significance level is 0.05), then state the correct decision regarding the null hypothesis and write a statement that correctly summarizes the conclusion in context.

Which of the following is not true about the coefficient of determination, $r ^ { 2 }$ ?

Explain what residuals are. Where do residuals come from? How are residuals calculated? Complete the table below by calculating the residuals for the following small data set. The linear model relating $x$ and $y$ is $y = 5 - 10 x$ . x y Residual 11 -100 5 -51 7 -63 4 -34

Which of the following is not true about residuals? If all the statements are true choose (d).

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Regression Analysis: Exploring Associations Between Variables

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

Filters

Exam 14: Inference for Regression

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

Which of the following statements is true about prediction intervals?

Which of the following statements is not true about the constant standard deviation condition of the linear regression model?

State the two conditions that must be satisfied, without exception, to make inferences using a linear model.

Suppose that you were presented with data showing the association between days absent from class and final class average. Which of the following residual plots below suggests that the Association between number of days absent from class and final class average is linear?

Test the hypothesis that the slope is zero (significance level is 0.05), then state the correct decision regarding the null hypothesis and write a statement that correctly summarizes the conclusion in context.

Which of the following is not true about the coefficient of determination, r2r ^ { 2 }r2 ?

Explain what residuals are. Where do residuals come from? How are residuals calculated? Complete the table below by calculating the residuals for the following small data set. The linear model relating xxx and yyy is y=5−10xy = 5 - 10 xy=5−10x . x y Residual 11 -100 5 -51 7 -63 4 -34

Which of the following is not true about residuals? If all the statements are true choose (d).

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Regression Analysis: Exploring Associations Between Variables

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

Filters

Which of the following is not true about the coefficient of determination, $r ^ { 2 }$ ?

Explain what residuals are. Where do residuals come from? How are residuals calculated? Complete the table below by calculating the residuals for the following small data set. The linear model relating $x$ and $y$ is $y = 5 - 10 x$ . x y Residual 11 -100 5 -51 7 -63 4 -34