Question

Please perform hypothesis test (F-test)

1. Below is the output corresponding to a data set containing one response variable, Y, and 4 predictor variables, var1, var2, var3, and var4. The var1, var2, and var3 predictor variables are quantitative and var4 is qualitative with levels A, B, and C.

Only use var1 and var2

Obs	Y	var1	var2	var3	var4
1	33.2	3.5	9	6.1	A
2	40.3	5.3	20	6.4	A
3	38.7	5.1	18	7.4	A
4	36.8	5.6	27	4.3	C
5	45.2	4.8	34	8.0	C
6	35.1	3.9	15	5.0	C

1. ) Perform the appropriate hypothesis test that compares a first-order model to the second-order model where both models only use the var1 and var2 predictor variables and the response variable Y. Make sure to perform all steps of the hypothesis test. Use a = 0.05 and critical value F = 3.16

H_{o (}first-order model): E(Y) = b₀ + b₁var1 + b₂var2

H_a: (second-order model):E(Y) = b₀ + b₁var1 + b₂var2 + b₃var1*var2 + b₄var1² + b₅var2²

How do you do an F-test on this? Thank you.

Answer 1

The F test is shown below:

The required F value is 3.973...

As the calculated F is more than F critical (3.16), so in this regard the null hypothesis is accepted...

End of the Solution...