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Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 9 - Correlation and Regression문제 9.1.9
9장, 문제 9.1.9

"In Exercises 9 and 10, identify the explanatory variable and the response variable.
9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight
loss."

검증된 단계별 안내
1
Step 1: Understand the problem by identifying the two variables involved. The problem mentions 'amounts of water consumed each day' and 'individual weight loss.' These are the two variables we need to classify as explanatory and response variables.
Step 2: Recall the definitions of explanatory and response variables. The explanatory variable is the one that is manipulated or used to explain changes in another variable, while the response variable is the outcome or the variable being measured.
Step 3: Analyze the relationship described in the problem. The nutritionist wants to determine if the 'amounts of water consumed each day' can be used to predict 'individual weight loss.' This suggests that the 'amounts of water consumed each day' is the variable being used to explain or predict changes in 'individual weight loss.'
Step 4: Assign the explanatory and response variables based on the analysis. The 'amounts of water consumed each day' is the explanatory variable because it is used to predict, and 'individual weight loss' is the response variable because it is the outcome being measured.
Step 5: Conclude that the explanatory variable is 'amounts of water consumed each day,' and the response variable is 'individual weight loss.' This classification helps in understanding the relationship being studied in the problem.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Explanatory Variable

The explanatory variable, also known as the independent variable, is the factor that is manipulated or categorized to observe its effect on another variable. In the context of the question, it refers to the amount of water consumed each day, as this is the variable the nutritionist is examining to see how it influences weight loss.
추천 영상:
가이드 코스
07:09
Intro to Random Variables & Probability Distributions

Response Variable

The response variable, or dependent variable, is the outcome that is measured to assess the effect of the explanatory variable. In this scenario, the response variable is individual weight loss, as it is the result that the nutritionist aims to predict based on the amount of water consumed.
추천 영상:
가이드 코스
07:09
Intro to Random Variables & Probability Distributions

Causation vs. Correlation

Understanding the difference between causation and correlation is crucial in statistics. Causation implies that changes in the explanatory variable directly cause changes in the response variable, while correlation indicates a relationship without implying direct influence. The nutritionist's study seeks to explore whether water consumption can causally affect weight loss, which requires careful analysis to establish.
추천 영상:
가이드 코스
05:43
Correlation Coefficient
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교과서 질문

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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교과서 질문

"[APPLET] Registered Nurse Salaries In Exercises 27–30, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Adapted from Payscale, Inc.)

27. Correlation Using the scatter plot of the registered nurse salary data shown below, what type of correlation, if any, do you think the data have? Explain.


"

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교과서 질문

8. In your own words, what does it mean to say "correlation does not imply causation"? List a pair of variables that have correlation but no cause-and-effect relationship.

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교과서 질문

In Exercise 25, remove the data for the international soccer player with a maximum weight of 170 kilograms and a jump height of 64 centimeters. Describe how this affects the correlation coefficient r.

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교과서 질문

4. For a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

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교과서 질문

2. Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

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