Testing multiple linear restrictions

Click For Summary
SUMMARY

This discussion focuses on testing multiple linear restrictions in a regression model involving four variables: Wealth, Divert, Race, and an unspecified fourth variable. The user seeks to understand how to construct null hypotheses when testing if Wealth (Beta1) is entirely responsible for the variation in the dependent variable Y while considering the contributions of Divert and Race. The proposed null hypotheses include H0: Beta1=1-Beta2, Beta3=0 and H0: Beta1=1, Beta3=0. The user concludes that testing for Beta1=1 is inappropriate if Divert contributes to the regression, as it would not accurately reflect the relationship between the variables.

PREREQUISITES
  • Understanding of multiple linear regression analysis
  • Familiarity with hypothesis testing and null hypotheses
  • Knowledge of F-tests in regression contexts
  • Basic concepts of variable contribution in regression models
NEXT STEPS
  • Research the construction of null hypotheses in multiple regression analysis
  • Learn about the implications of variable exclusion in regression models
  • Study the application of F-tests for comparing restricted and unrestricted models
  • Explore the effects of multicollinearity on regression coefficients
USEFUL FOR

Statisticians, data analysts, and researchers involved in regression modeling and hypothesis testing, particularly those working with multiple linear regression and variable significance testing.

mrcleanhands
If I have 4 variables in my multiple regression and I'm told to test whether one is significant, and 3 others are not what would I do with the one left over?

I thought it would be easy as I could just test whether for H0: variable 1>0, variable 2,3 =0

But what if I'm told to restrict variable 1 so that under H0 it must =1?

If you think about it variable cannot = 1 unless there is no contribution from variable 4 (which I'm told I must "take into account"). This is because my Y variable has a maximum value of 100 and my variable 1 also has a maximum value of 100.

By forcing variable=1 I'm saying that the whole of the change in Y is caused by variable 1. But we have already agreed that variable 4 is a contributer. So how do I "take it into account" when building a restricted and unrestricted model?


If I exclude variable 4 from both the restricted and unrestricted than variable 1 won't be equal to 1, and if I include it won't be = 1 either!
 
Physics news on Phys.org
Allow me to restate this in better terms...

I have 3 variables in an oversimplified model. Wealth, Divert, Race.
So that Y = a function of Beta1*(Wealth) + Beta2*(Divert) + Beta3*(Race).

My Y variable ranges from 0-100. Beta1 also varies from 0-100. I'm trying to test whether Wealth is 100% responsible AND that race does not matter for the variation in Y, after taking into account the variable "Divert". I'm going to construct a restricted and unrestricted model and then conduct an F-test.Would it make sense for me to setup the null hypothesis thus:

(H-0) is: Beta1=1-Beta2, Beta3=0
H-1 would be: Beta 1 ≠ 1-Beta2 and / or Beta3≠0.I was told I could also use:
set null (H-0) as: Beta1=1, Beta3=0
H-1 would be: Beta 1 ≠ 1 and / or Beta3≠0.But this doesn't make any sense to me as if we want to account for "Divert" then it is silly to test for Beta1=1. Beta1 will not equal one if "Divert" contributes to the regression, it will only equal the variation in Y which is unexplained by "Divert" (1-Divert).Is my thinking correct?
 

Similar threads

Undergrad Expected coefficient change from simple to multiple linear regression
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Linear regression and random variables
  • · Replies 30 ·
2
Replies
30
Views
5K
Undergrad Linear regression, feature scaling, and regression coefficients
  • · Replies 8 ·
Replies
8
Views
3K
MHB Multiple choice test : random variable
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Linear Model with independent categorical variable
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Linear Regression, Population, Sample
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Collinearity between predictors: what happens under the hood
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Coefficient sign flip in linear regression with correlated predictors
  • · Replies 13 ·
Replies
13
Views
5K
Undergrad Linear regression with error term
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Regression line with zero slope and average as best prediction
  • · Replies 2 ·
Replies
2
Views
2K