I have a question in a paper that involves calculating the maximum yield based on a linear model in which yield is explained by the amount of something being transported plus the number of days it is being transported for (plus an intercept). The thing is being transported for at least 3 days and not more than 10, and the amount is a fixed value.
There is a negative coefficient for days and a positive one for amount. Both are significant in the presence of each other (as well as the intercept).
The R output is provided, so it includes the estimate of coefficient, the standard error, the T value and the Pr(>|t|) value.
How do you approach this? My initial thought was that, given that there is a negative coefficient for days, that it would be the maximum at 3 days - as each day passes the yield would decrease. But then I had second thoughts about this. Should I be taking the standard error into account? If so, how? Would prediction/confidence intervals be possible? I don't think so because I don't know the value of $n$, but someone else might know better!