Nullity test

#1
Good evening,

I have a problem i can't solve. The data is:
n=25
Y_i= Beta1 + Beta2 * x_i + Beta3 * z_i + epsilon_i
B_hat = (2.341 1.616 0.014)
SSR= 233.726
SST= 5843.15
sqrt(X*Xt)^(-1)_(3,3)= 0.00107 (square root of the bottom right coefficient of the (X*Xt)^(-1) matrix).

The questions i'm on are:
1) Give an unbiased estimator of sigma^2
2) Do the simultaneous nullity teston all betas except beta_1 with alpha = 1% (test H0: Beta_2 = Beta_3 = 0)

For the estimator i guess it's:
Σ((y_i- y_hat)^2)/(n-1) = SST / (n-1)

But for the simultaneous nullity test, i don't understand how to do it and have no clue in my courses.

Sorry for my english and if it is unclear,
Thanks for your help
 
Last edited:

noetsi

Fortran must die
#2
I have not heard of the nullity test before. What method is this, regression. Do you mean the test of the null hypothesis when you say the nullity test?
 
#3
I have not heard of the nullity test before. What method is this, regression. Do you mean the test of the null hypothesis when you say the nullity test?
Yes sorry, the null hypothesis test. Here it would be H0: Beta_2 = Beta_3 = 0.
Thanks for the answer
 

noetsi

Fortran must die
#4
In linear regression you would run a t test and then interpret the resulting p value associated with it to see if its below the alpha level. If it is you reject the null (which I am sure you know). :) But how you would manually calculate the p value I do not know. All that I have read about this is that the calculations of p are very complex. I have never seen it calculated manually.
 
#5
In linear regression you would run a t test and then interpret the resulting p value associated with it to see if its below the alpha level. If it is you reject the null (which I am sure you know). :) But how you would manually calculate the p value I do not know. All that I have read about this is that the calculations of p are very complex. I have never seen it calculated manually.
Ok i'll keep thinking then :) thanks anyway