12.93 A factory is estimating its yearly profit size based on several explanatory factors. Based on a sample of 55 observations, the following model was estimated by least squares:

yn = 2074.838 + 29.335x1 - 14.436x2 - 7.354x3 + 45.932x4

+ 5.991x5 + 1.041x6 - 2.545x7 - 0.910x8 R2 = 0.9723 where yn = yearly profit x1 = number of production units x2 = materials cost x3 = machine maintenance cost x4 = return on equity x5 = investment on each employee x6 = self-financing capacity x7 = degree of technical endowment x8 = personnel cost per employee Also obtained by least squares from these data was the fitted model:

yn = 1455.547 + 32.793x1 - 10.901x2 - 5.739x3

+ 62.325x4 R2 = 0.6986 The variables x5, x6, x7, and x8 are measures of the secondary explanatory factors of the factory. Test, at the 1% level, the null hypothesis that they do not contribute to explaining yearly profit, given that x1, x2, x3, and x4 are also to be used.