What is the formula for the correlation coefficient, *r*?
$r = \frac{1}{n-1} \sum_{i=1}^{n} (\frac{x_i - \bar{x}}{s_x}) (\frac{y_i - \bar{y}}{s_y})$
In the formula for *r*, what do $\bar{x}$ and $\bar{y}$ represent?
$\bar{x}$ and $\bar{y}$ are the means of the x and y variables, respectively.
In the formula for *r*, what do $s_x$ and $s_y$ represent?
$s_x$ and $s_y$ are the standard deviations of the x and y variables, respectively.
In the formula for *r*, what does 'n' represent?
n is the number of data points.
What does $\sum$ represent in the formula for *r*?
$\sum$ represents the summation of the expression that follows.
Explain the concept of correlation vs. causation.
Correlation indicates a relationship between variables, but does not prove that one variable causes the other. Other factors may be involved.
Explain the impact of outliers on the correlation coefficient, *r*.
The correlation coefficient, *r*, is not resistant to outliers. A single outlier can drastically change the value of *r*.
Explain the concept of linearity in correlation.
*r* only measures linear relationships. A strong *r* doesn't mean there's no relationship, just no linear one.
How do you interpret the strength of correlation based on the value of *r*?
Values of *r* closer to 1 or -1 indicate a stronger linear relationship, while values closer to 0 indicate a weaker linear relationship.
Explain how to find the correlation coefficient using a TI-84 calculator.
Enter x-values in L1 and y-values in L2. Go to STAT > CALC > LinReg(ax+b). Ensure 'DiagnosticOn' is enabled in the MODE menu to see the *r* value.
What is the correlation coefficient?
A value, *r*, that measures the strength and direction of a linear relationship between two variables. Ranges from -1 to 1.
Define positive correlation.
A relationship where as one variable increases, the other tends to increase.
Define negative correlation.
A relationship where as one variable increases, the other tends to decrease.
What does *r* = 0 indicate?
No linear correlation between the two variables.
What is a scatterplot?
A graphical representation of the relationship between two variables.
