Recall from Week 2: Correlation Coefficient, r The Correlation coefficient, r, is a measure of the strength and direction of a linear relationship between 2 variables X and Y Ranges between –1 and 1 • The closer to –1, the stronger the negative linear relationship • The closer to 1, the stronger the positive linear relationship • The closer to 0, the weaker the linear relationship (Also called Standardised Covariance i.e. invariant to units of measure)

Sure, I can explain the correlation coefficient in more detail.

The correlation coefficient, often denoted by 'r', is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0.

1. A correlation of -1 indicates a perfect negative correlation, meaning as one variable goes up, the other goes down.

2. A correlation of 1 indicates a perfect positive correlation, meaning as one variable goes up, the other one also goes up.

3. A correlation of 0 indicates that there is no linear relationship between the variables.

Here are the steps to calculate the correlation coefficient:

Step 1: Find the mean of x, and the mean of y.

Step 2: Subtract the mean of x from every x value (call them "a"), do the same for y (call them "b").

Step 3: Calculate: a*b, a^2 and b^2 for every value.

Step 4: Sum up a*b, sum up a^2 and sum up b^2.

Step 5: Divide the sum of a*b by the square root of [(sum of a^2) * (sum of b^2)].

The result is the correlation coefficient.

Remember, correlation does not imply causation. Just because two variables correlate does not mean that changes in one variable are responsible for changes in the other.