Question

A study was conducted on a high-pressure inlet fogging method for a gas turbine engine. Researchers considered two models. Partial output is provided below.

Source	Df	SS	MS	F
Regression	5	148526859	29705372	94
Error	61	19370350	317547
Total	???	167897208

Source	Df	SS	MS	F
Regression	???	142586570	47528857	???
Error	63	25310639	401756
Total	???	167897208

Answer the following questions rounding off at the nearest integer.

The number of observations collected for the study is equal to

The number of predictors considered in the reduced model is equal to

The F-test for global utility of the reduced model is equal to

Results suggest that the complete model provides additional information compared to the reduced model. In fact, the F-test for nested models is equal to  which is greater than the rejection region F(alpha =0.05) with numerator degrees of freedom equal to  and denominator degrees of freedom equal to  .

Answer 1

The number of observations collected for the study is equal to =5+61+1 =67

The number of predictors considered in the reduced model is equal to =142586570/47528857 =3

The F-test for global utility of the reduced model is equal to =47528857/401756 =118.30 ~118

Partial F test statistic =((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) =

9.353409

numerator df =(c-r) =					2
and denominator df =(n-c-1) =					61

  In fact, the F-test for nested models is equal to 9 which is greater than the rejection region F(alpha =0.05) with numerator degrees of freedom 2 equal to  and denominator degrees of freedom equal to 61 .