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Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 9 - Correlation and RegressionProblem 9.1.10
Chapter 9, Problem 9.1.10

"In Exercises 9 and 10, identify the explanatory variable and the response variable.
10. An actuary at an insurance company wants to determine whether the number of hours of safety driving classes can be used to predict the number of driving accidents for each
driver."

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1
Step 1: Understand the definitions of explanatory and response variables. The explanatory variable (also called the independent variable) is the variable that is used to explain or predict changes in another variable. The response variable (also called the dependent variable) is the outcome or variable that is being predicted or explained.
Step 2: Identify the variables mentioned in the problem. Here, the actuary is interested in the number of hours of safety driving classes and the number of driving accidents for each driver.
Step 3: Determine which variable is used to predict the other. The problem states that the actuary wants to see if the number of hours of safety driving classes can be used to predict the number of driving accidents.
Step 4: Assign the explanatory variable as the number of hours of safety driving classes because it is the predictor variable.
Step 5: Assign the response variable as the number of driving accidents because it is the outcome that is being predicted.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Explanatory Variable

The explanatory variable, also known as the independent variable, is the factor that is manipulated or considered as the cause in a study. It is used to explain or predict changes in another variable. In this context, it is the number of hours of safety driving classes.
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Response Variable

The response variable, or dependent variable, is the outcome or effect that is measured in a study. It depends on the explanatory variable and reflects the result of interest. Here, it is the number of driving accidents for each driver.
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Predictive Relationship

A predictive relationship involves using one variable to forecast or estimate another. Understanding this helps determine how changes in the explanatory variable might influence the response variable, such as predicting accidents based on safety class hours.
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Related Practice
Textbook Question

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

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Textbook Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.

28. Total Assets Construct a 90% prediction interval for the total assets in federal defined benefit plans in Exercise 18 when the total assets in IRAs are \$6400 billion."

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Textbook Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.

30. New Vehicle Sales Construct a 99% prediction interval for new vehicle sales for Honda in Exercise 20 when the number of new vehicles sold by Toyota is 2159 thousand."

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Textbook Question

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

46
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Textbook Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.

22. Mean Hourly Wage Construct a 95% prediction interval for the mean hourly wage in Exercise 12 when the median hourly wage is \$21.50."

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Textbook Question

"Graphical Analysis In Exercises 1–3, use the figure.

1. Describe the total variation about a regression line in words and in symbols."

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