Understanding Sample Correlation and Pearson Coefficient
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Questions and Answers

What does a correlation coefficient close to zero imply?

  • A non-linear relationship may exist between the two variables (correct)
  • No relationship exists between two variables
  • A linear relationship exists between the two variables
  • A strong positive relationship exists between the two variables

    • In statistics, what does Spearman’s rank correlation measure?

  • Causal relationships
  • Population parameter
  • Non-linear monotonic relationships (correct)
  • Linear relationships

    • Why is the interpretation of the correlation coefficient considered difficult?

  • It is heavily dependent on sample size
  • It is not sensitive to outliers
  • It doesn't measure any relationship between variables
  • It cannot explain causation (correct)

    • What is the purpose of performing a test of significance (such as R: cor.test()) on a correlation coefficient?

    <p>To assess if there is evidence against a null hypothesis of no correlation</p> Signup and view all the answers

    Which statistical method is mentioned as a better way to understand the relationship between variables than the correlation coefficient?

    <p>R-squared</p> Signup and view all the answers

    What does a high sensitivity to outliers mean for a correlation coefficient?

    <p>It can cause the correlation coefficient to be highly influenced by extreme data points</p> Signup and view all the answers

    What does a correlation coefficient of -0.99 between water content and calorific value indicate?

    <p>A strong negative relationship</p> Signup and view all the answers

    What does the small p-value (p < 0.0001) tell us?

    <p>There is strong evidence against the null hypothesis</p> Signup and view all the answers

    In the Bagasse example, what can we conclude about the relationship between water content and calorific value from the correlation coefficient?

    <p>There is a strong negative relationship</p> Signup and view all the answers

    How does the p-value affect our understanding of the relationship between water content and calorific value?

    <p>It provides strong evidence against the null hypothesis</p> Signup and view all the answers

    Based on the information provided, what can be inferred about calorific value as water content increases?

    <p>Calorific value decreases</p> Signup and view all the answers

    Why is a regression model needed to answer more complex questions about the relationship between water content and calorific value?

    <p>To understand how calorific value changes with water content</p> Signup and view all the answers

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