yi=ß1xi1+ß2xi2+ß3xi3+ß4xi4+ei

For the hypothesisH0:ß2=1,ß3=ß4

(a) propose a test...

Question

yi=ß1xi1+ß2xi2+ß3xi3+ß4xi4+ei

For the hypothesisH0:ß2=1,ß3=ß4

(a) propose a test statistic (with specific, rather than general, notation.)
(b) state what is its distribution under the null and why(c) explain the conditions under which you would rejectH0(d) show how your test statistic can be computed from two regressions.

David · Accepted Answer

yi =ß1xi1 +ß2xi2 +ß3xi3 +ß4xi4 +ei  
For the hypothesis H0 : ß2=1, ß3= ß4  
(a) Propose a test statistic (with specific, rather than general, notation.) Answer: 
For null hypothesis: H0 : ß2=1 
Test statistics; t = 
   ̂
                    ̂ 
 = 
   ̂   
                    ̂ 
, where    ̂ is an estimator of    
The test statistic t is likely to follow t-distribution with (n-4) degree of freedom, where n 
denote number of observation. 
For null hypothesis: H0: ß3= ß4 or (ß3- ß4)= 0 
Test statistics;

yi=ß1xi1+ß2xi2+ß3xi3+ß4xi4+ei For the hypothesisH0:ß2=1,ß3=ß4 (a) propose a test statistic (with specific, rather than general, notation.) (b) state what is its distribution under the null and why (c)...

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