Multivariate linear regression

In summary, to test the hypothesis that beta1=0 and beta2=0, a t test can be used in multiple linear regression with n-3 degrees of freedom. Each variable can be tested separately using PROC REG in SAS, with the p value for each test saved to a new dataset. However, caution must be taken when interpreting results if the variables are highly correlated.
  • #1
Trilli@n
2
0
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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  • #2
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.
 
  • #3
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?
 

1. What is multivariate linear regression?

Multivariate linear regression is a statistical method used to model and analyze the relationship between multiple independent variables and a dependent variable. It is an extension of simple linear regression, which only considers one independent variable.

2. When is multivariate linear regression used?

Multivariate linear regression is typically used when there are multiple independent variables that may influence a dependent variable. It is commonly used in fields such as economics, social sciences, and business to study the relationship between several factors and a specific outcome.

3. How does multivariate linear regression differ from simple linear regression?

The main difference between multivariate linear regression and simple linear regression is the number of independent variables. Simple linear regression only considers one independent variable, while multivariate linear regression considers two or more. This allows for a more complex and nuanced analysis of the relationship between variables.

4. What are the assumptions of multivariate linear regression?

The assumptions of multivariate linear regression include linearity, independence of errors, normality of errors, homoscedasticity (equal variance) of errors, and absence of multicollinearity (high correlation) among the independent variables.

5. How is the accuracy of a multivariate linear regression model evaluated?

The accuracy of a multivariate linear regression model is typically evaluated by examining the coefficient of determination (R-squared), which indicates the proportion of the variation in the dependent variable that is explained by the independent variables. Other metrics, such as the root mean square error (RMSE) and adjusted R-squared, may also be used to assess the model's performance.

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