2,9-E "Inference for Slope" Quiz

A random sample of 30 companies on the Forbes 500 list was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated using regression. A least-squares regression line was fitted to the data using statistical software, with sales as the explanatory variable and profits as the response variable. Assume that the conditions for inference are met. Here is the output from the software: Which of the following is an appropriate interpretation of the number 0.092498?

• For each increase of $100,000 in profits, the predicted sales increases by $9,249.80.
• For each increase of $100,000 in sales, the predicted profit increases by $9,249.80.
• Sales of $100,000 correspond to predicted average profits of $9,249.80.
• The actual profit typically varies by about $9249.80 from the profit predicted with the least squares regression line using x = sales.
• The actual sales typically varies by about $9249.80 from the sales predicted with the least squares regression line using x = profit.

To see if students with longer feet tend to be taller, a random sample of 25 students was selected from a large high school. For each student, x = foot length (cm) and y = height (cm) were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-square regression analysis using these data: Which of the following expressions best represents the margin of error of a 90% confidence interval for the slope of the population regression line?

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• 1.701(0.0106)
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Below is a regression analysis of the number of burglaries in 2016 (response variable) on the student enrollment (explanatory variable) for 17 randomly selected four-year public universities in the United States. Assume that the conditions for regression inference have been met. Which of the following is an appropriate interpretation of the number 22.5012?

• The actual number of students enrolled typically varies by about 22.5012 from the number predicted with the least squares regression line using x = number of burglaries.
• The typical distance between the predicted burglaries and the least-squares regression line is about 22.5012.
• The typical distance between the observed values for student enrollment and values for enrollment predicted by the regression equation is about 22.5012.
• The actual number of burglaries typically varies by about 22.5012 from the number predicted with the least squares regression line using x = student enrollment.
• The sum of the squared deviations between the observed number of burglaries and the number of burglaries predicted by the regression equation is about 22.5012.

When checking the conditions for regression inference, which of the following is evidence that the condition of equal standard deviation of y for each value of x has not been satisfied?

• The residual plot has a distinctly curved shape.
• The residual plot shows a group of randomly scattered points.
• The histogram of residuals is skewed to the right.
• Small value of the explanatory variable are associated with small residuals, and large values of the explanatory variable are associated with large residuals.
• The scatterplot has a distinctly curved shape.

Twenty students volunteered to take a fitness test. Below is the computer regression analysis of the relationship between x = how fast they can run a mile (in mph) and y = how high they can jump (in inches). We want to know if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these. What is the P-value of this test?

• 0.006
• 0.012
• 0.041
• 0.082
• 0.164

To see if students with longer feet tend to be taller, a random sample of 25 students was selected from a large high school. For each student, x = foot length (cm) and y = height (cm) were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-square regression analysis using these data: Which of the following is the equation of the least-squares regression line for predicting height from foot length?

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To see if students with longer feet tend to be taller, a random sample of 25 students was selected from a large high school. For each student, x = foot length (cm) and y = height (cm) were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-square regression analysis using these data: The slope beta of the population regression line describes

• the exact increase in height (cm) for students at this high school when foot length increases by 1 cm.
• the average increase in foot length (cm) for students at this high school when height increases by 1 cm.
• the average increase in height (cm) for students at this high school when foot length increases by 1 cm.
• the average increase in foot length (cm) for students in the sample when height increases by 1 cm.
• the average increase in height (cm) for students in the sample when foot length increases by 1 cm.