lme(measurement~ D*Temp, random = ~Temp|ID, data=dt)

y1= 0.25+0.8*D+0.57*Temp-0.0023*D*Temp for Case 1 D is significant, interaction is significant

y2= 0.03+0.32*D+0.21*Temp-0.0076*D*Temp for Case 2 D is not significant, interaction is significant

Notes: Samples were tested at 4 different temperatures (0, 15, 30, 37 degrees). D and Temp are numerical and ID is categorical. The residuals were normally distributed, there were no violation for homoscedasticity and multicollinearity.

Q1= Some people suggest that you don't need to interpret the main effect even it is significant while you have significant interaction. If this is correct statement, how does equation would work if we want to compute, especially for Temp 0 since there will be only D and Temp remains?

Q2= If main effect should be also interpreted, should we only interpret for the significant one or all of them?

Q3=If I need to keep the equation as above and I do not need to interpret the main effect for case 1 or 2, how should I solve the equation for the Temp at 0 degree, i.e. y= 0.03+0.32*D+0.21*Temp-0.0076*D*0will be y= 0.03+0.32*D. In this case, do I say the y is positively influenced by D although I do not interpret the main effect?

If I am not mistaken, if I need to interpret the effect of D while keeping the Temp constant and evaluate as (0.32-0.0076Temp)D. What confuses me here is that if we write 0 for Temp then how do we explain the equation? Other question is that if we dont need to interpret main effect individually, how can I explain what equation indicates?

PS: If I keep Temp 0 then the effect of D is positive and it doesn't make sense at all. Logically, as D increases it should negatively effect the response.

Thank you for your kind help.

Best, Tim