Question 1

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

Accepted Answer

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

Question 2

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.
  
-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 3

Use the following information to answer the question. A high school girls cross country coach performs a regression to predict the finish times of runners in the 10k event 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.
  
-The coach wants to predict the finish time of his top runner who trained for 145 minutes the previous week. Should the coach use a confidence interval or a prediction interval?

Accepted Answer

A) Prediction Interval 
B) Confidence Interval 
A) Prediction Interval 
B) Confidence Interval

Question 4

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 H₀. There is enough evid

Question 5

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 6

Of the following conditions, which one can fail yet produce a regression model that is reasonably good, in many cases, if the sample size is large?

Accepted Answer

A) Normality of errors 
B) Independence of errors 
C) Linearity 
D) None of these 
A) Normality of errors 
B) Independence of errors 
C) Linearity 
D) None of these

Question 7

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 best describes whether the condition for normality of errors does or does not hold for the linear regression model.

Accepted Answer

A) The residual plot shows no trend, therefore the normality condition is not satisfied. 
B) The residual plot does not display a fan shape, therefore the normality condition is satisfied. 
C) The QQ plot mostly follows a straight line, therefore the normality condition is satisfied. 
D) The residual plot shows no trend, therefore the normality condition is satisfied. 
A) The residual plot shows no trend, therefore the normality condition is not satisfied. 
B) The residual plot does not display a fan shape, therefore the normality condition is satisfied. 
C) The QQ plot mostly follows a straight line, therefore the normality condition is satisfied. 
D) The residual plot shows no trend, therefore the normality condition is satisfied.

Question 8

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.
  
-Choose the correct null and alternative hypothesis to test whether there is an association between final class average and number of message board posts.

Accepted Answer

A) H0: There is a linear association between the number of message board posts and the final class average. Ha: There is no linear association between the number of message board posts and the final class average. 
B) H0: The correlation is positive. Ha: The correlation is zero. 
C) H0: There is no linear association between the number of message board posts and the final class average. Ha: There is a positive linear association between the number of message board posts and the final class average. 
D) None of these. 
A) H0: There is a linear association between the number of message board posts and the final class average. Ha: There is no linear association between the number of message board posts and the final class average. 
B) H0: The correlation is positive. Ha: The correlation is zero. 
C) H0: There is no linear association between the number of message board posts and the final class average. Ha: There is a positive linear association between the number of message board posts and the final class average. 
D) None of these.

Question 9

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 slope (rounded to the nearest hundredth)? Does this interval support the theory that the slope is zero? Write a statement that summarizes your answer in context.

Accepted Answer

(0.86, 1.36). This interval does not sup

Question 10

Use the following information to answer the question. A high school boys cross country coach performs a regression to predict the finish times of runners in the 10k event 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.
  
-Suppose the coach's top runner trained for 180 minutes the previous week. If this runner participates in the 10k event, what is the coach's expected finish time for this runner? Can he be reasonably confident that this runner will beat the previous season's record of 43 minutes?

Accepted Answer

A) Expected finish time is 38.84 minutes. The coach can be confident that this runner will beat the previous season's record of 43 minutes because the interval contains the value of 43 minutes. 
B) Expected finish time is 38.84 minutes. The coach cannot be confident that this runner will beat the previous season's record because the interval contains the value of 43 minutes. To be confident the interval would have to lie completely below 43 minutes. 
C) Expected finish time is 65.84 minutes. The coach can be confident that this runner will beat the previous season's record of 43 minutes because the interval contains the value of 43 minutes. 
D) Expected finish time is 65.84 minutes. The coach cannot be confident that this runner will beat the previous season's record because the interval contains the value of 43 minutes. To be confident the interval would have to lie completely below 43 minutes. 
A) Expected finish time is 38.84 minutes. The coach can be confident that this runner will beat the previous season's record of 43 minutes because the interval contains the value of 43 minutes. 
B) Expected finish time is 38.84 minutes. The coach cannot be confident that this runner will beat the previous season's record because the interval contains the value of 43 minutes. To be confident the interval would have to lie completely below 43 minutes. 
C) Expected finish time is 65.84 minutes. The coach can be confident that this runner will beat the previous season's record of 43 minutes because the interval contains the value of 43 minutes. 
D) Expected finish time is 65.84 minutes. The coach cannot be confident that this runner will beat the previous season's record because the interval contains the value of 43 minutes. To be confident the interval would have to lie completely below 43 minutes.

Question 11

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 - 10x.

Accepted Answer

The residual is the variation from the l

Question 12

Environmental biologists studying the relationship between the number of owls in a forested region and the number of field mice in the region believe that the deterministic component of the relationship is a straight line. A scatterplot shows that even though the general trend is linear, the points do not fall exactly on a straight line. Which of the following factors might account for the random component of this regression model?

Accepted Answer

A) Variation in the size of the mice might cause variation in the amount of mice consumed by owls. 
B) Different size owls might affect the number of mice eaten. 
C) Variability might appear in the instrument used to count mice. 
D) All of these are possible factors that could account for the random component of the regression model. 
A) Variation in the size of the mice might cause variation in the amount of mice consumed by owls. 
B) Different size owls might affect the number of mice eaten. 
C) Variability might appear in the instrument used to count mice. 
D) All of these are possible factors that could account for the random component of the regression model.

Question 13

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.
  
-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 H0. 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 H0. 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 H0. 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 H0. 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 H0. 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 H0. 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 H0. 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 H0. 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.

Question 14

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 15

Use the following information to answer the question. Below is the scatterplot showing the association between miles driven in a semi truck (x), and the amount of tread wear on the tires (y). The residual plot of the data is also shown along with a QQ plot of the residuals.
    
-Based on the plots provided, choose the statement that best describes whether the condition for constant standard deviation does or does not hold for the linear regression model.

Accepted Answer

A) The residual plot does not display a fan shape-- the residual plot is consistent with the claim of constant standard deviation. 
B) The scatterplot shows a linear trend-- the scatterplot is not consistent with the claim of constant standard deviation. 
C) The QQ plot mostly follows a straight line-- the QQ plot is consistent with the claim of constant standard deviation. 
D) The residual plot shows no trend-- the residual plot is not consistent with the claim of constant standard deviation. 
A) The residual plot does not display a fan shape-- the residual plot is consistent with the claim of constant standard deviation. 
B) The scatterplot shows a linear trend-- the scatterplot is not consistent with the claim of constant standard deviation. 
C) The QQ plot mostly follows a straight line-- the QQ plot is consistent with the claim of constant standard deviation. 
D) The residual plot shows no trend-- the residual plot is not consistent with the claim of constant standard deviation.

Question 16

Which of the following is not a condition of the linear regression model?

Accepted Answer

A) Normality of errors 
B) Linearity 
C) Residuals must be normally distributed 
D) Constant Standard Deviation 
A) Normality of errors 
B) Linearity 
C) Residuals must be normally distributed 
D) Constant Standard Deviation

Question 17

Use the following information to answer the question. A random sample of 30 couples who were also new home owners were asked to report the cost of their first house and their combined age when they married. The output of a regression analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are satisfied.
  
-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) Reject H0. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost. 
B) Reject H0. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost. 
C) Fail to reject H0. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost. 
D) Fail to reject H0. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost. 
A) Reject H0. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost. 
B) Reject H0. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost. 
C) Fail to reject H0. There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost. 
D) Fail to reject H0. We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost.

Question 18

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.
  
-State the slope of the regression line. Write a sentence explaining what this slope means in this context.

Accepted Answer

The slope is 0.92. On average,

Question 19

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.
  
-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 20

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.
  
-Choose the correct decision regarding the null hypothesis and the correct conclusion. State your conclusion using a significance level of 5%.

Accepted Answer

A) Fail to reject H0. There is enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
B) Fail to reject H0. There is not enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
C) Reject H0. There is enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
D) Reject H0. There is not enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
A) Fail to reject H0. There is enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
B) Fail to reject H0. There is not enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
C) Reject H0. There is enough evidence to conclude that the final class average is positively associated with the number of message board posts. 
D) Reject H0. There is not enough evidence to conclude that the final class average is positively associated with the number of message board posts.

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

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 residuals? If all the statements are true choose (d).

Of the following conditions, which one can fail yet produce a regression model that is reasonably good, in many cases, if the sample size is large?

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 - 10x.

Which of the following is not a condition of the linear regression model?

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

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 residuals? If all the statements are true choose (d).

Of the following conditions, which one can fail yet produce a regression model that is reasonably good, in many cases, if the sample size is large?

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 - 10x.

Which of the following is not a condition of the linear regression model?

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