are the same as for multiple linear regression with an intercept, except that the definitions given in Multiple Regression without Intercept of df Res, SS Res, correlation vector B, hat matrix H, R 2, etc. In the case of regression without an intercept, the values of various statistics such as AIC, AICc, SBC, VIF, Tolerance, Cook’s D, DFFITS, etc. Comparison with Regression with Intercept The second argument R2 in the dfRes, dfReg and dfTot are optional (actually, this argument is not used). RegSBC(R1, R2, con, aug) = Schwarz Bayesian Criterion (SBC) RegAICc(R1, R2, con, aug) = corrected Akaike’s Information Criterion (AICc) RegAIC(R1, R2, con, aug) = Akaike’s Information Criterion (AIC) RegE(R1, R2, con) = n × 1 residuals vector for y values in R2 RegY(R1, R2, con) = n × 1 vector of predicted values for y values in R2 RegCoeff(R1, R2, con) = k × 2 range consisting of the regression coefficient vector followed by a vector of standard errors of these coefficients if con = FALSE (the output is a k+1 × 2 range if con = TRUE, to include the intercept coefficient and its standard error) LEVERAGE(R1, con) = column range which contains the diagonal elements of the hat matrix In the following R1 is an n × k array containing the X sample data and R2 is an n × 1 array containing the y sample data. Real Statistics Functions: The following Real Statistics functions, described in Real Statistics Capabilities for Multiple Regression, can be used for regression without an intercept when the con argument is set to FALSE ( con = TRUE is the default). LINEST(R1, R2, con, TRUE) = array function which outputs a 5 × k range where k = the number of independent variables (plus 1 if con = TRUE), as described Multiple Regression Analysis in Excel.Įxcel’s Regression data analysis tool, as described in Multiple Regression Analysis in Excel, you can force the constant term to be zero by checking the Constant is Zero option. If R3 is omitted it defaults to the range R2. TREND(R1, R2, R3, con) = array function which predicts the y values corresponding to the x values in R3 based on the regression line based on the x values stored in array R2 and y values stored in array R1. The following Excel functions, described previously in Multiple Regression Analysis in Excel, can be used for regression without an intercept when the con argument is set to FALSE ( con = TRUE is the default).