Faulty Use of Correlation On the basis of the scatter diagram below, explain what is wrong with the following statement: “Because the linear correlation coefficient between age and median income is 0.012, there is no relation between age and median income.”
Table of contents
- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
- 6. Normal Distribution and Continuous Random Variables2h 11m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
- 9. Hypothesis Testing for One Sample3h 57m
- 10. Hypothesis Testing for Two Samples4h 50m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- 11. Correlation1h 24m
- 12. Regression1h 50m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA1h 57m
11. Correlation
Scatterplots & Intro to Correlation
Problem 4.1.2
Textbook Question
The variable is the variable whose value can be explained by the value of the explanatory variable.
Verified step by step guidance1
Understand the terminology: In statistics, we often deal with two types of variables in a relationship—an explanatory variable and a response variable.
The explanatory variable (also called independent variable) is the one that is used to explain or predict changes in another variable.
The variable whose value can be explained or predicted by the explanatory variable is called the response variable (also known as the dependent variable).
So, the response variable depends on or responds to changes in the explanatory variable.
In summary, the variable whose value can be explained by the explanatory variable is the response variable.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Dependent Variable
The dependent variable is the outcome or response variable whose value depends on or is explained by changes in another variable. It is what you measure in an experiment or study to see the effect of the explanatory variable.
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Explanatory Variable
The explanatory variable, also known as the independent variable, is the variable that is manipulated or categorized to observe its effect on the dependent variable. It helps explain variations in the dependent variable.
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Cause-and-Effect Relationship
This concept refers to the relationship where changes in the explanatory variable cause changes in the dependent variable. Understanding this helps in interpreting how one variable influences another in statistical analysis.
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Scatterplots & Intro to Correlation
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