Exam 1

1. Metainformation

   Tag	Value
   file	Descriptive-statistics_uva-correlation-579-en_uva-correlation-579-en
   name	uva-correlation-579-en
   section	Descriptive statistics/Summary Statistics/Bivariate statistics/Correlation
   type	schoice
   solution	FALSE, FALSE, TRUE, FALSE
   Type	Calculation
   Language	English
   Level	Statistical Literacy

   Question

   Calculate the Pearson correlation coefficient, if given

   • Mean of X: 0.5
   • Average of Y: 0.5
   • Standard deviation of X: 0.2
   • Standard deviation of Y: 0.25
   • Covariance between X and Y: 0.039
   
   
   1. FALSE: -0.57
   2. FALSE: -0.36
   3. TRUE: 0.78
   4. FALSE: 1
   
   

   Solution

   To calculate the Pearson correlation coefficient, we need not only the means and standard deviations of the two variables, but also the covariance between them. Here is the formula we will use:

   $r = \frac{\text{cov}(X, Y)}{\sigma_X \sigma_Y}$

   in which: - $r$ the Pearson correlation coefficient is. - $\text{cov}(X, Y)$ the covariance between $X$ and $Y$ is. - $$sigma_X$ is the standard deviation of $X$ is. - $$sigma_Y$ the standard deviation of $Y$ is.

   
   
   1. 0.57: Incorrect
   2. 0.36: Incorrect
   3. 0.78: Correct
   4. 1: Incorrect