Error in lm.fit(x,y,offset = offset, singular.ok,...) 0 non-NA cases with boxcox formula

The error message

lm.fit(x,y,offset = offset, singular.ok = singular.ok, ...) : 0 (non-NA) cases

is generated by the lm(y ~ x) command when variables x or y (or both) have only NAs.
Here is an example:

n <- 10
x <- rnorm(n,1)
y <- rep(NA,n)
lm(y ~ x)

Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases

In your code I suggest to test (just before your lm commands) if one of your variables has all NAs using:

all(is.na(x))
all(is.na(y))
all(is.na(y^trans))

In my example:

all(is.na(y))
[1] TRUE

The error can be triggered by NA's in your data or a bad transformation

#From the mtcars dataset
mpg.reg3 <- lm(mpg ~ cylinders + displacement + horsepower + weight + acceleration + year + origin, data=Auto, na.action=na.exclude)

Notice the na.action= argument. Setting this to na.exclude will allow the lm function to ignore NA's in your data. Another option is na.omit which acts in a slightly different manner.

The other problem may be a bad transformation of your data- double check your interaction terms and manipulations.