Finding predictions using biglm without finding errors
biglm calls model.frame which "all the variables in the formula are included in the data frame" see documentation for model.frame. This is the issue that comes up when predict is called on the biglm class. It looks for those values in the predict function. To get around this you can just create a variable and encode it with 0. See below...

data(trees)
ff&lt;-log(Volume)~log(Girth)+log(Height)

chunk1&lt;-trees[1:10,]
chunk2&lt;-trees[11:20,]
chunk3&lt;-trees[21:31,]

a &lt;- biglm(ff,chunk1)
summary(a)

#produces same error
chunk2 &lt;- select(chunk2, -Volume)
predict(a, chunk2)

#Fixed
chunk2$Volume &lt;- 0
predict(a, chunk2)