Partial Correlation and Confounding Variables
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Questions and Answers

What does partial correlation measure in probability theory and statistics?

  • The standard deviation of a sample
  • The degree of association between two random variables, with the effect of controlling variables removed (correct)
  • The absolute strength of the relationship between two random variables
  • The variance of a single random variable

What problem does using a partial correlation coefficient aim to avoid?

  • Underestimating the effect size
  • Overfitting the data
  • Ignoring outliers in the data
  • Misleading results caused by uncontrolled confounding variables (correct)

Why might using the correlation coefficient alone give misleading results?

  • If the sample size is too small
  • If there is another confounding variable that is numerically related to both variables of interest (correct)
  • If there is no linear relationship between the variables
  • If the correlation coefficient is negative

In what context would failing to control for wealth when computing a correlation coefficient between consumption and income lead to misleading results?

<p>When income might be numerically related to wealth which in turn might be numerically related to consumption (A)</p> Signup and view all the answers

What does multiple regression provide unbiased results for, but does not give a numerical value for?

<p>The effect size (C)</p> Signup and view all the answers

What is the range of possible values for the correlation coefficient?

<p>-1 to 1 (B)</p> Signup and view all the answers

What does a correlation coefficient close to +1 indicate?

<p>A strong positive linear relationship (C)</p> Signup and view all the answers

In algebraic notation, how is the correlation coefficient calculated for two variables x and y?

<p>$r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}$ (C)</p> Signup and view all the answers

What does a correlation coefficient close to -1 indicate?

<p>A strong negative linear relationship (D)</p> Signup and view all the answers

What does the scatter diagram reveal about the strength of the linear relationship between two variables?

<p>The closer the points lie to a straight line, the stronger the linear relationship. (C)</p> Signup and view all the answers

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