Python Tutorial: Simple Linear Regressions

Want to learn more? Take the full course at https://learn.datacamp.com/courses/introduction-to-time-series-analysis-in-python at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- In this video, you'll learn about simple linear regressions of time series. A simple linear regression finds the slope, beta, and intercept, alpha, of a line that's the best fit between a dependent variable, y, and an independent variable, x. The x's and y's can be a two-time series. A linear regression is also known as Ordinary Least Squares, or OLS, because it minimizes the sum of the squared distances between the data points and the regression line. Regression techniques are very common, and therefore there are many packages in Python that can be used. In statsmodels, there is OLS. In numpy, there is polyfit, and if you set degree equals 1, it fits the data to a line, which is a linear regression. Pandas has an ols method, and scipy has a linear regression function. Beware that the order of x and y is not consistent across packages. All these packages are very similar, and in this course, you will use the statsmodels OLS. Now you'll regress the returns of the small cap stocks on the returns of large cap stocks. Compute returns from prices using the "pct_change" method in pandas. You need to add a column of ones as a dependent, right-hand side variable. The reason you have to do this is because the regression function assumes that if there is no constant column, then you want to run the regression without an intercept. By adding a column of ones, statsmodels will compute the regression coefficient of that column as well, which can be interpreted as the intercept of the line. The statsmodels method "add constant" is a simple way to add a constant. Notice that the first row of the return series is NaN. Each return is computed from two prices, so there is one less return than price. To delete the first row of NaN's, use the p