Python Tutorial : Quantifying Linear Relationships

Want to learn more? Take the full course at https://learn.datacamp.com/courses/introduction-to-linear-modeling-in-python at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- In previous exercises, we've used data visualization to explore the relationship between two variables. In this lesson, we introduce methods from descriptive statistics, including "correlation", as a way of quantifying linear trends in the data. Before reviewing any statistics, let's pause and note that visualization is always a great first step. Here, plotting 3 data sets reveals 3 very different trends. The data on the left is said to be highly correlated. As x increases, y increases with it. The linear trend is apparent. The data on the far right shows that as x changes, y does not change in the same way. For this data, x and y are said to be "not correlated". The data in the middle is ambiguous. The correlation value is a quantitative measure of how strong of a linear relationship there is between two variables in your data. To understand correlation, we need to step back and review some statistics. In previous courses, you saw how to compute measures of central tendency and spread of a single variable. The mean is a measure of the center. For a measure of spread, try subtracting the mean from every data point: the results are called deviations. If we average these, they tend to cancel out to zero, so we square them first and then average. The result is called the variance. But now the units are not the same as the data, so we take the square root. The result is the standard deviation. While the variance measures how a single variable varies, covariance measures how two variables "vary together". To compute it, first compute the deviation arrays, dx and dy, from each of two arrays, x and y. Then, take the product of each pair of deviations, and lastly, average all those products. For each deviation product, if b