 Samalla vuonna maailmastolleen os Taasot on vähän erittäin beden järvelle. Silloin tietysti samalla asioiden katastoundosta ja F-t queste. In the F-t test in the regression analysis we have two models. One is the constraint model and another one is the unconstrained model. Here model two is the more general unconstrained model and model one is a special case of model two mielenkiintoisia, koska me otamme model 1 ja model 2, kuten että nämä reikerss- ja koeffisissa, jotka ovat esim. täällä, ovat todella ympäristöjä model 1, koska me ei oteta nämä varioita. Sitten me otamme matkaisuja, me kalkkulamme summa- ja r-squareta nämä modelilla. Me katsoimme se, että ympäristö, että me otamme statistiikkaa, joka tuntuu f-distimusin. In maximum likelihood estimates, we don't have the r-square, we don't have the sum of squares, instead we use the divine statistic. So here in Kramer's paper we have two models, so model one is the constraint model, model two is the unconstraint model because we have this coefficient here that is estimated here it is constrained to be zero. So we have one degree of freedom difference between these two models. Then we can calculate the likelihood ratio test of whether adding this one more parameter increases the model fit more than what can be expected by chance only by comparing these deviances or minus two times log likelihood. So model two is the unrestrictive model, model one is the restrictive model. We calculate the difference between the model deviances which is 3.79 and that difference follows the chi-square distribution with one degree of freedom because there is only one parameter difference here. And the p-value for that would be 0.05 which says that there is no statistically significant difference between the models that's on the border of 0.05 level and it's also shown here that this is not very significant here. In contrast to F's test which always if you have one parameter gives you the same exact p-value as t-test, these statistic, they are significant statistic here from z-test and the likelihood ratio p-value, they don't necessarily have the exact same value because these are based on large sample approximations that may not work exactly as intended in small samples. So there can be some scenarios like here we have a significant coefficient p is less than 0.05 but here we have p that is more than 0.05 but it's on the boundary so we could just say that there is weak evidence for the existence of this relationship.