First calculate the array of error terms E (range O4:O14) using the array formula I4:I14 – M4:M14. The standard error of each of the coefficients in B can be calculated as follows.
Y-hat, can then be calculated using the array formula Per Property 1 of Multiple Regression using Matrices, the coefficient vector B (in range K4:K6) can be calculated using the array formula: The matrix ( X T X) -1 in range E17:G19 can be calculated using the array formula Range E4:G14 contains the design matrix X and range I4:I14 contains Y. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.Example 1: Calculate the linear regression coefficients and their standard errors for the data in Example 1 of Least Squares for Multiple Regression (repeated below in Figure using matrix techniques.įigure 1 – Creating the regression line using matrix techniques The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options.
This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data.
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