Multiple regression analysis in excel 2016

In particular, the standard error of the intercept b 0 (in cell K9) is expressed by the formula =SQRT(I17), the standard error of the color coefficient b 1 (in cell K10) is expressed by the formula =SQRT(J18), and the standard error of the quality coefficient b 2 (in cell K11) is expressed by the formula =SQRT(K19).Д®xcel Functions: The functions SLOPE, INTERCEPT, STEYX and FORECAST donвЂ™t work for multiple regression, but the functions TREND and LINEST do support multiple regression as does the Regression data analysis tool. Then just as in the simple regression case SS Res = DEVSQ(O4:O14) = 277.36, df Res = n вЂ“ k вЂ“ 1 = 11 вЂ“ 2 вЂ“ 1 = 8 and MS Res = SS Res/ df Res= 34.67 (see Multiple Regression AnalysisВ for more details).Д«y the Observation following Property 4В it follows that MS ResВ ( X T X) -1В is the covariance matrix for the coefficients, and so the square root of the diagonal terms are the standard error of the coefficients. First calculate the array of error terms E (range O4:O14) using the array formula I4:I14 вЂ“ 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.ДЇigure 1В вЂ“ Creating the regression line using matrix techniques

Multiple regression analysis in excel 2016