Exam 14: Inference for Regression

Choose the statement(s)that are not true about the estimators for slope and intercept of a regression line when the conditions of the linear model hold. If each statement is true choose (d).

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

Use the following information to answer the question. A humanities professor is interesting in learning whether there is a positive association between average online homework scores and the final class average in an online humanities course. The computer output below shows the results from a regression model in which the final class average was predicted by the average online homework score. 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.

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. -Suppose the coach's top runner trained for 145 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 time she had at the last meet of 51 minutes?

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. -What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context.

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 linearity is satisfied.

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.

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?

Which of the following statements is not true about prediction intervals?

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

Consider the following statement: "When the conditions of the linear model hold, the estimators for slope and intercept are unbiased." What is meant by the word unbiased in this context?

Use the following information to answer the question. A humanities professor is interesting in learning whether there is a positive association between average online homework scores and the final class average in an online humanities course. The computer output below shows the results from a regression model in which the final class average was predicted by the average online homework score. 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 average online homework scores.

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. -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?

Explain how a residual plot can be useful in determining whether the condition for linearity and the condition for a constant standard deviation have been satisfied.

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. -If the intercept was 0 and the slope was 1, what would that say about the association?

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

Suppose that you were presented with data showing the association between days absent from class and final class average. Use the following residual plots, based on the data, to answer the question. -Which of the residual plots above would suggest that the association between number of days absent from class and final class average is linear? Explain.

Explain the difference between confidence intervals and prediction intervals. Be sure to include the type of situation in which each type of interval would be used. Which interval is likely to be wider and why?

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 constant standard deviation does or does not hold for the linear regression model.

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.