![]() Whenever we use the ordinary least square method to estimate the intercept and slope coefficients of the regression model, we assume that the sampling distribution of our sample estimates (intercept and slopes) follow a normal distribution, given that our sample size is large, i.e. But, while conducting various hypotheses tests, I come across the terms: sample means, sampling distribution of mean, central limit theorem (CLT), the law of large numbers, sample statistic, population parameter, and various distributions. Pair-trading or statistical arbitrage is used to exploit such deviations in the spread.įirst of all, I would like to express that I am not an expert in the statistical distributions or statistics. If any deviation occurs, both price series will correct this deviation to revert back to the mean-spread (spread is assumed to be mean reverting or stationary). If two price series are cointegrated, the spread between these two price series (or the difference between two price-series) should be constant (or evolving gradually over the time). It means that both the prices need not move in the same direction every day for the existence of the cointegration. They will have to revert back to an equilibrium price eventually. Whereas, if they are cointegrated, both the prices cannot wander off in opposite direction for very long. Both the prices will go up or go down every day in synchrony. If both the price series are positively correlated, it means that both series move in synchrony. Now, we would discuss the differences of these terms. Join today and get 150 hours of free compute per month.After describing the differences between the correlation and the cointegration, suppose that there are only two time-series (For example, daily price data of two series). Spin up a notebook with 4TB of RAM, add a GPU, connect to a distributed cluster of workers, and more. Saturn Cloud is your all-in-one solution for data science & ML development, deployment, and data pipelines in the cloud. By following these steps, you can create informative and visually appealing plots that communicate the relationships in your data. We have also demonstrated how to display the equation of the regression line on the plot itself using the geom_text() function. In this blog post, we have shown you how to add a linear regression line to a scatter plot in R using the ggplot2 library. We use the round() function to round the coefficients to two decimal places for readability. The first coefficient is the y-intercept, and the second coefficient is the slope of the line. The coef() function extracts the coefficients of the linear regression model using the lm() function. The text is generated using the paste() function, which combines the text strings and the coefficients of the linear regression equation. The aes() function specifies the position of the label on the plot, and the label argument specifies the text to display. This code adds a text label to the plot using the geom_text() function. Ggplot ( mtcars, aes ( x = hp, y = mpg )) + geom_point () + geom_smooth ( method = "lm" ) + geom_text ( aes ( x = 250, y = 25, label = paste ( "y =", round ( coef ( lm ( mpg ~ hp, data = mtcars )), 2 ), "x +", round ( coef ( lm ( mpg ~ hp, data = mtcars )), 2 )))) Please refer to this code as experimental only since we cannot currently guarantee its validity ⚠ This code is experimental content and was generated by AI. You will also need the ggplot2 package, which can be installed using the following command: To follow along with this tutorial, you will need to have R and RStudio installed on your machine. This line is called the regression line and is represented by the equation y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The goal of linear regression is to find the line that best fits the data points. ![]() In simple linear regression, there is only one independent variable. Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. But how can you display the equation of the regression line on the plot itself? In this blog post, we will show you how to do just that using R. One common task in data analysis is to fit a linear regression model and plot the data points along with the regression line. ![]() | Miscellaneous ⚠ content generated by AI for experimental purposes only How to Print Equation of Linear Regression on Plot in RĪs a data scientist or software engineer, you know the importance of visualizing data to understand patterns and relationships. ![]()
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