Question

Multivariable testing (MVT) was shown to improve the quality of carbon-foam rings used in nuclear missile housings. The rings are produced via a casting process that involves mixing ingredients, oven curing, and carving the finished part. One type of defect analyzed was the number (y) of black streaks in the manufactured ring. Two variables found to impact the number of defects were turntable speed ( x1 , in revolutions per minute) and cutting-blade position ( x2 , in inches from center).

1) The researchers discovered an interaction between the blade position and turntable speed. Pick a regression model that incorporates this interaction.
a. E[y] = β0 + β1x1 + β2x2
b. E[y] = β0 + β1x1 + β2x1x2
c. E[y] = β0 + β1x1x2
d. E[y] = β0 + β1x1 + β2x2 +β3x1x2

b) The researchers wanted to test if the interaction term is significant in the model. Perform this test with α=0.05 and n=17.
Note: use the notation B1 = 0 to represent β1=0 and so on. If you need ≠ then type B1 /= 0 for β1≠0 with the spaces!.
1. H0:  vs Ha:  
2. α = 0.05
3. t = 4.326
4. Critical t=  
5. Conclusion:
Fail to reject H0
Reject H0
Interpretation:
a. There is not sufficient evidence to support that the interaction term is significant.
a. There is sufficient evidence to support that the interaction term is significant.

Answer 1

1. The regression model that incorporates this interaction :

d) E[y] = β₀ + β₁x₁ + β₂x₂ +β₃x₁x₂

b) To test against

The value of the test statistic =

At 5% level of significance, critical value =

Since , so we reject H₀ at 5% level of significance.

Interpretation :

There is sufficient evidence to support that the interaction term is significant.