# Testing the sum of regression coefficients

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## Testing the sum of regression coefficients

 My son has to test the hypothesis that the sum of the coefficients in a linear regression equation equals 1. That would be the null hypothesis, I suppose. The equation has two predictors, so in fact he wants to test the null hypothesis that B1+B2=1. How you do this? I am extremely busy at the moment so I am transmitting the query to this forum. Thanks in advance. Hector ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: Testing the sum of regression coefficients

 Hi Hector: > My son has to test the hypothesis that the sum of the coefficients in a > linear regression equation equals 1. That would be the null hypothesis, I > suppose. The equation has two predictors, so in fact he wants to test the > null hypothesis that B1+B2=1. How you do this? I am extremely busy at the > moment so I am transmitting the query to this forum. (sorry, I'm cooking right now because I have people invited for dinner tonight, I can't extend a lot on the topic). Using the same logic I use when I want to test particular hypotheses concerning beta coefficients in logistic regression, I guess the idea is to compute a generalised t test in the form:     (b1+b2+...+bk)-1 t=----------------------       SE(sum(bi)) The SE is the tricky part. I think it must be something like: SE=SQRT(SE^2(b1)+SE^2(b2)+...+SE^2(bk)-R12SE(b1)*SE(b2)-R12SE(b1)*SE(b3)....) To get the correlation among coefficients, you need the following syntax (notice the /OUTFILE=COVB(Coefficients) ): DATASET DECLARE Coefficients. REGRESSION   /MISSING LISTWISE   /STATISTICS COEFF OUTS R ANOVA ZPP   /CRITERIA=PIN(.05) POUT(.10)   /NOORIGIN   /DEPENDENT salario   /METHOD=ENTER salini tiempemp expprev   /OUTFILE=COVB(Coefficients) . You will get a SD&covariance matrix you need to turn into correlations using MCONVERT. I promise that tomorrow morning (CET) I will extend my skimpy explanation a bit more. Also, I will take a look at my regression books. Now, a mussaka awaits me. Best regards, Marta García-Granero ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: Testing the sum of regression coefficients

 Use GLM with the x's as the covariates ( there are no factors) Setup and then hit paste. Add the following: \lmatrix = "b1 + b2" all 0 1 1. \kmatrix = 1. F. Michael Speed Professor Director of Online Learning Department of Statistics Associate Dean for Technology Mediated Instruction College of Science TAMU  979-845-3182 -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Marta García-Granero Sent: Tuesday, November 27, 2007 12:22 PM To: [hidden email] Subject: Re: Testing the sum of regression coefficients Hi Hector: > My son has to test the hypothesis that the sum of the coefficients in a > linear regression equation equals 1. That would be the null hypothesis, I > suppose. The equation has two predictors, so in fact he wants to test the > null hypothesis that B1+B2=1. How you do this? I am extremely busy at the > moment so I am transmitting the query to this forum. (sorry, I'm cooking right now because I have people invited for dinner tonight, I can't extend a lot on the topic). Using the same logic I use when I want to test particular hypotheses concerning beta coefficients in logistic regression, I guess the idea is to compute a generalised t test in the form:     (b1+b2+...+bk)-1 t=----------------------       SE(sum(bi)) The SE is the tricky part. I think it must be something like: SE=SQRT(SE^2(b1)+SE^2(b2)+...+SE^2(bk)-R12SE(b1)*SE(b2)-R12SE(b1)*SE(b3)....) To get the correlation among coefficients, you need the following syntax (notice the /OUTFILE=COVB(Coefficients) ): DATASET DECLARE Coefficients. REGRESSION   /MISSING LISTWISE   /STATISTICS COEFF OUTS R ANOVA ZPP   /CRITERIA=PIN(.05) POUT(.10)   /NOORIGIN   /DEPENDENT salario   /METHOD=ENTER salini tiempemp expprev   /OUTFILE=COVB(Coefficients) . You will get a SD&covariance matrix you need to turn into correlations using MCONVERT. I promise that tomorrow morning (CET) I will extend my skimpy explanation a bit more. Also, I will take a look at my regression books. Now, a mussaka awaits me. Best regards, Marta García-Granero ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD