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

Larson 8th Edition

Ch. 9 - Correlation and Regression

Problem 9.1.38b

Chapter 9, Problem 9.1.38b

Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.
b. Other Factors: The relationship between the variables is caused by a third variable.

Verified step by step guidance

Step 1: Identify a real-life data set that demonstrates a cause-and-effect relationship influenced by a third variable. For example, consider a data set showing the relationship between ice cream sales and drowning incidents, where the third variable is temperature.

Step 2: Define the variables in the data set. For instance, Variable 1 could be 'Ice Cream Sales,' Variable 2 could be 'Drowning Incidents,' and the third variable (causal factor) could be 'Temperature.'

Step 3: Describe each variable in detail. For example, 'Ice Cream Sales' represents the number of ice creams sold, 'Drowning Incidents' represents the number of reported drowning cases, and 'Temperature' represents the average daily temperature.

Step 4: Explain the cause-and-effect relationship. For instance, higher temperatures lead to increased ice cream sales and more people swimming, which could result in more drowning incidents. Thus, the relationship between ice cream sales and drowning incidents is not direct but is influenced by the third variable, temperature.

Step 5: Write a paragraph summarizing the findings. Include the description of each variable and explain how the third variable (temperature) causes the observed relationship between the other two variables.

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Key Concepts

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

Cause-and-Effect Relationship

A cause-and-effect relationship indicates that one variable (the cause) directly influences another variable (the effect). Understanding this relationship is crucial for establishing how changes in one variable can lead to changes in another. For example, an increase in temperature (cause) may lead to an increase in ice cream sales (effect). Identifying such relationships helps in making predictions and understanding underlying mechanisms.

Confounding Variable

A confounding variable is an external factor that may affect both the independent and dependent variables, potentially misleading the interpretation of the cause-and-effect relationship. For instance, if studying the relationship between exercise and weight loss, diet could be a confounding variable that influences both. Recognizing confounding variables is essential to ensure that the observed relationship is not spurious.

Data Set Analysis

Data set analysis involves examining and interpreting data to identify patterns, relationships, and insights. This process includes descriptive statistics, inferential statistics, and visualizations to summarize and understand the data. In the context of cause-and-effect relationships, analyzing a data set helps to validate hypotheses and assess the strength and significance of the relationships between variables.

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Related Practice

Textbook Question

"Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 11-20, use the data to (a) find the coefficient of determination r^2 and interpret the result,

12. [APPLET] Median and Mean Hourly Wages The table shows the median and mean hourly wages (in dollars) in 10 states in a recent year. The equation of the regression line is y = 1.208x + 1.495. (Source: U.S. Census Bureau)

Textbook Question

Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.

a. Direct Cause-and-Effect: Changes in one variable cause changes in the other variable.

Textbook Question

"Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 11-20, use the data to (b) find the standard error of estimate s_e and interpret the result.

Textbook Question

"[APPLET] For Exercises 2–9, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years. (Source: U.S. Bureau of Labor Statistics)

6. Use the regression equation that you found in Exercise 5 to predict the average annual salary of postsecondary library science teachers when the average annual salary of librarians is \$61,000."

Textbook Question

c. Coincidence: The relationship between the variables is a coincidence.

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