1. Tobacco budworm Heliothis virescens The tobacco budworm, Heliothis virescens (Fabricius), is a native species and is found throughout the eastern and southwestern United States, though it is also known from California. It generally overwinters successfully only in southern states. However, it occasionally survives cold climates in greenhouses and other sheltered locations. Tobacco budworm disperses northward annually, and can be found in New England, New York, and southern Canada during the late summer. It also occurs widely in the Caribbean, and sporadically in Central and South America.

2. Experiment: Reaction of the tobacco budworm Heliothis virescens to doses of the pyrethroid trans-cypermethrin. Batches of 20 moth of each sex were exposed for three days to the pyrethroid and the number in each batch that were dead or knocked down was recorded.

3. Experiment data Dose: represented by variable x = 1,2,4,8,16,32 Gender: represented by variable y = M, F Proportion of knocked moths:  (x,y)

4. Effect of dose on survival rate Effect is highly significant and explains most of the variation in the data. Still, we see that the gender information can improve the prediction. Model 1: logit [  (x,y)] =  +  x

5. Effect of moth gender on survival rate Effect is significant but can’t explain the variation in data: the residual deviance is almost the same as the null deviance. Collinearity: Notice that significance of both parameters decreased. This is because they both have the same effect (constant level) and R cannot decide which one to choose. Model 2: logit [  (x,y)] =  +  y

6. Individual effects of moth gender and dose on survival rate The same dose-slope  for males and females, different intercepts  and . Effects of both factors are significant and explain really well the data variation. Model 3: logit [  (x)] =  +  x +  y

7. Combined effect of gender-dose on survival rate Different dose-slopes  i  for males and females, intercept  is the same. All parameters are significant and explain really well the data variation. Model 4: logit [  (x)] =  +  1 xI {y=M} +  2 xI {y=F}

8. Effect of moth gender and dose on survival rate Different dose-slopes (  1 ) and  for males and females, different intercepts (  +  ) and . Effects of both factors are significant and explain really well the data variation. The AIC suggests that this model is inferior to Model 4: additional parameter is not worth the fit improvement. Model 5: logit [  (x)] =  +  x +  y +  1 xI {y=M}