Yield of corn, alfalfa, clover with two fertilizers

Usage

data("heady.fertilizer")

Format

A data frame with 81 observations on the following 3 variables.

crop: crop
rep: replicate (not block)
P: phosphorous, pounds/acre
K: potassium, pounds/acre
N: nitrogen, pounds/acre
yield: yield

Details

Heady et al. fit two-variable semi-polynomial response surfaces for each crop.

Clover and alfalfa yields are in tons/acre. The clover and alfalfa experiments were grown in 1952.

Corn yields are given as bu/acre. The corn experiments were grown in 1952 and 1953. The same test plots were used in 1953 and in 1952, but no fertilizer was applied in 1953–any response in yield is due to residual fertilizer from 1952.

All experiments used an incomplete factorial design. Not all treatment combinations were present.

Source

Earl O. Heady, John T. Pesek, William G. Brown. (1955). Crop Response Surfaces and Economic Optima in Fertilizer Use. Agricultural Experiment Station, Iowa State College. Research bulletin 424. Pages 330-332. https://lib.dr.iastate.edu/cgi/viewcontent.cgi?filename=12&article=1032&context=ag_researchbulletins&type=additional

References

Pesek, John and Heady, Earl O. 1956. A two nutrient-response function with determination of economic optima for the rate and grade of fertilizer for alfalfa. Soil Science Society of America Journal, 20, 240-246. https://doi.org/10.2136/sssaj1956.03615995002000020025x

Examples

if (FALSE) { # \dontrun{

library(agridat)
data(heady.fertilizer)
dat <- heady.fertilizer

libs(lattice)
xyplot(yield ~ P|crop, data=dat, scales=list(relation="free"),
       groups=factor(paste(dat$N,dat$K)), auto.key=list(columns=5),
       main="heady.fertilizer", xlab="Phosphorous")

# Corn. Matches Heady, p. 292
d1 <- subset(dat, crop=="corn")
m1 <- lm(yield ~ N + P + sqrt(N) + sqrt(P) + sqrt(N*P), data=d1)
summary(m1)


# Alfalfa. Matches Heady, p. 292.  Also Pesek equation 3, p. 241
d2 <- subset(dat, crop=="alfalfa")
m2 <- lm(yield ~ K + P + sqrt(K) + sqrt(P) + sqrt(K*P), data=d2)
summary(m2)
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  1.8735521  0.1222501  15.326  < 2e-16 ***
## K           -0.0013943  0.0007371  -1.891 0.061237 .
## P           -0.0050195  0.0007371  -6.810 5.74e-10 ***
## sqrt(K)      0.0617458  0.0160142   3.856 0.000196 ***
## sqrt(P)      0.1735383  0.0160142  10.837  < 2e-16 ***
## sqrt(K * P) -0.0014402  0.0007109  -2.026 0.045237 *


# Clover. Matches Heady, p. 292.
d3 <- subset(dat, crop=="clover")
m3 <- lm(yield ~ P + sqrt(K) + sqrt(P) + sqrt(K*P), data=d3)
summary(m3)

# Corn with residual fertilizer. Matches Heady eq 56, p. 322.
d4 <- subset(dat, crop=="corn2")
m4 <- lm(yield ~ N + P + sqrt(N) + sqrt(P) + sqrt(N*P), data=d4)
summary(m4)

  libs(rgl)
  with(d1, plot3d(N,P,yield))
  with(d2, plot3d(K,P,yield))
  with(d3, plot3d(K,P,yield))
  with(d4, plot3d(N,P,yield)) # Mostly linear in both N and P
  close3d()

} # }