Testing Hypotheses in Multivariate Linear Regression Using SAS?

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SUMMARY

This discussion focuses on testing hypotheses in multivariate linear regression using SAS. The model presented is y = beta0 + beta1 x1 + beta2 x2 + eps, where eps follows a normal distribution. To test the hypothesis that beta1=0 and beta2=0, a t-test is employed, with degrees of freedom calculated as n-3. The SAS code provided utilizes PROC REG to perform the regression analysis and hypothesis testing, while also addressing the importance of considering multicollinearity between x1 and x2.

PREREQUISITES
  • Understanding of multivariate linear regression concepts
  • Familiarity with hypothesis testing using t-tests
  • Proficiency in SAS programming, specifically PROC REG
  • Knowledge of multicollinearity and its implications in regression analysis
NEXT STEPS
  • Learn how to implement multivariate regression diagnostics in SAS
  • Explore methods for detecting and addressing multicollinearity in regression models
  • Research how to extract and save p-values from regression tests in SAS
  • Study advanced hypothesis testing techniques in multivariate contexts
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Data analysts, statisticians, and researchers involved in regression analysis and hypothesis testing using SAS, particularly those working with multivariate models.

Trilli@n
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I have a model y= beta0 + beta1 x1 + beta2 x2 + eps, eps~N(0,1).

How to test hypothesis beta1=0 ? Is the same test for beta2=0?
 
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you can use a t test just like you do in simple linear regression,
except the degrees of freedom is n-3 not n-2,
You can test each variable separately.

you have to be careful about any conlcusions you make for example if x1 and x2 are highly correlated.
 
Can someone help me to do this in SAS?
Is this correct?

PROC REG DATA = dataset;
MODEL y = x1 x2;
test x1=0 ;
test x2=0;
run;

How can I save p value from each test to a new data?
 

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