#########################
# GENERAL LINEAR F TEST #
#########################

# clean all variables
rm(list=ls())

# read in data
setwd("c:/Documents/Classes/Econ4230/R_and_Stata/")
library(readxl)
data = read_excel("Data/prodfn.xlsx")

# transform variables
data$lnQ = log(data$Q)      # add a column with ln(Q)
data$lnK = log(data$K)      # add a column witn ln(K)
data$lnL = log(data$L)      # add a column with ln(L)

# Ftest manually, constructing new regressions
# Source: Gujarati p.249-250

# unrestricted regression 
unrestricted <- lm(lnQ ~ lnL + lnK, data = data)

# restrict to H0: Beta2 = Beta3, transform the model & OLS
data$x1star = data$lnK + data$lnL
restricted = lm(lnQ ~ x1star, data = data)

# calculate F stat
RSSu = sum(unrestricted$residuals^2)
RSSr = sum(restricted$residuals^2)
N = nrow(data)
K = 3
J = 1
Fval = ((RSSr-RSSu)/J) / (RSSu/(N-K))

# In Matrix form, with R*Beta = q
# Source: Farnsworth - Econometrics in R Tutorial, p.26

library(car)
unrestricted = lm(lnQ ~ lnL + lnK, data = data)
q = c(0)
R = rbind(c(0,1,-1))
linearHypothesis(unrestricted, R, q)