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# Regressions with Various Functional Forms #
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# 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)

# simple regressions
results1 = lm(Q ~ L, data=data)
results2 = lm(lnQ ~ lnL, data = data)
#results2 = lm(Q ~ L -1, data=data)    # -1 takes the intercept out
#results3 = lm(Q ~ L + K, data=data)   # multivariate regression

# display results
# results1               # show only coefficients
summary(results1)        # show whole table of regression results
summary(results2)        # show whole table of regression results

x = sort(data$L)
#y = sort(results1$fitted.values)
y = sort(exp(results2$fitted.values))

plot(data$L, data$Q, 
     xlab = "L", 
     ylab = "Q", 
     main = "Production Function Regression")
lines(x, y)       # add fitted regression line