The linear correlation coefficient, r, is a numerical measure of the strength of the relationship between two variables representing quantitative data.

Yes.

is this true or false? The linear correlation coefficient, r, is a numerical measure of the strength of the relationship between two variables representing quantitative data.

To calculate the linear correlation coefficient, r, between two quantitative variables, you can follow these steps:

1. Gather your data: Collect pairs of values for the two variables you are interested in studying. Make sure you have a sufficient number of data points.

2. Calculate the mean (average) for each variable: Add up all the values for each variable and divide by the total number of data points. Let's call these means x̄ and ȳ.

3. Calculate the standard deviation for each variable: Subtract the mean for each variable from each data point, square the differences, add up all the squared differences, divide by (n - 1), and take the square root. Let's call these standard deviations s𝑥 and s𝑦.

4. Calculate the covariance between the two variables: For each pair of data points, subtract the mean of x from the x-value, and subtract the mean of y from the y-value. Multiply these differences together and add them up. Divide by (n - 1). Let's call this covariance C𝑥𝑦.

5. Calculate the linear correlation coefficient, r: Divide the covariance (C𝑥𝑦) by the product of the standard deviations (s𝑥 and s𝑦). The formula for r is: r = C𝑥𝑦 / (s𝑥 * s𝑦).

6. Analyze the value of r: The linear correlation coefficient, r, ranges from -1 to +1. A positive value indicates a positive correlation (as one variable increases, the other tends to increase), while a negative value indicates a negative correlation (as one variable increases, the other tends to decrease). The closer r is to -1 or +1, the stronger the correlation is, while r close to 0 indicates a weak or no correlation.

It's worth noting that the linear correlation coefficient measures only the strength and direction of the linear relationship between the variables. It does not imply causation between the two variables.