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. 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
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