How to predict multiple future values in a linear model in R?

Question

So i currently have a data set consisting of the Year, Credit Hours, and Number of students. I have been trying to predict future credit hours by the number of students.

   df <- data.frame("year = c(2018,2019,2020,2021), "student" = c(1000,1200,1350,1450), "credit" = c(4000,4300,4730,4250))


    mod <- lm(credit ~ year + student, data = df)
    summary(mod)

I would like to predict the number of credit hours for the next couple of years, lets just say 2022:2025, that also factors in predicted number of students. Is there a way to do this?

year	credit	student
2018	4000	1000
2019	4300	1200
2020	4730	1350
2021	4250	1450
2022	NA	NA
2023	NA	NA
2024	NA	NA
2025	NA	NA

In other words, how can I use a linear model in R to predict all of these NA values? I can do this in a simple linear regression no problem, but cannot seem to get it to work in multiple form.

Answer 1

To predict $credit_{t+1}$, you need $year_{t+1}$ (which you have) and $student_{t+1}$ (which you don't have). So first you need to create a model (or a formula) to predict that.

Looking are your data, the student vector is $(1000,1200,1350,1450)$ which could be (for example) a marginally decreasing series such as: $(.., 200,150,100)$ halving by each year, thus the following changes could be $(50,25,12.5,6.25)$.

Therefore the forecasted values for student could be $(1500,1525,1537.5, 1543.75)$. You can also create a trend model (in levels, $student = f(year)$ or differences, $Δstudent = f(year)$ ) for the same goal.

Now you have the values for all independent variables in the forecasting period, therefore after the predict option, you can apply the coefficients of the model to the full data to obtain the future values of credit hours. This explanation doesn't deal with the goodness of fit of that last model ($credit = f(year, student)$).