Correlation Coefficient Calculation for Two Variables

Calculate the correlation coefficient between the two variables given the data (x: 1, 2, 3, 4, 5, 6; y: 2, 4, 7, 9, 12, 14).

In this problem, you are tasked with calculating the correlation coefficient between two sets of data. The correlation coefficient is a statistical measure that describes the degree to which two variables move in relation to one another. It is a key concept in statistical analysis and helps in understanding the strength and direction of a linear relationship between two variables. In simpler terms, it tells us how two variables are related and the nature of their relationship, whether positive or negative, strong or weak.

To tackle this problem, you'll need to apply the formula for the Pearson correlation coefficient, which is one of the most common methods used to measure the linear correlation between two variables. This involves calculating the mean of each variable, determining the covariance between the two variables, and then dividing by the product of their standard deviations. It is important to understand each step's purpose and how they contribute to the final correlation value, which will range between -1 and 1.

A correlation close to +1 implies a strong positive correlation, meaning both variables tend to move in the same direction. A correlation close to -1 indicates a strong negative correlation, meaning as one variable increases, the other tends to decrease. A correlation around 0 suggests no linear relation between the variables. Understanding these concepts is crucial, as it provides insights into the relationships between variables, which can be applied to various fields such as economics, finance, and natural sciences.