How to fit a quadratic equation to a plot obtained from plotmeans function in R

Question

We are analyzing fixed effects heterogeneity across years of a panel database ("mydata") containing values of an economic explained value depending on 12 independent variables. Data correspond to the period 2007-2017 and 142 countries. We use function plotmeans from package gplots being the script as follows:

plotmeans(D ~ Year, main="Heterogeineity across years", data=mydata)

We obtain the graph hereunder:

Is there any function/script on R that can fit the obtained plot into a quadratic curve providing its equation coefficients?

Answer 1

First, fit a quadratic curve:

df <- data.frame(year = c(1,2,3,4,5,6,7,8,9),
                 D = c(35,26,19,6,1,3,5,12,17))

fit<-lm(D~poly(year,2,raw=TRUE), df)

> summary(fit)

Call:
lm(formula = D ~ poly(year, 2, raw = TRUE), data = df)

Residuals:
   Min     1Q Median     3Q    Max 
-2.987 -1.872 -0.039  1.545  4.305 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                  52.786      3.400   15.53  4.5e-06 ***
poly(year, 2, raw = TRUE)1  -17.103      1.561  -10.96  3.4e-05 ***
poly(year, 2, raw = TRUE)2    1.469      0.152    9.65  7.1e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.67 on 6 degrees of freedom
Multiple R-squared:  0.959, Adjusted R-squared:  0.946 
F-statistic: 71.1 on 2 and 6 DF,  p-value: 6.65e-05

Next count the value of year estimation:

quadratic = fit$coefficient[3]*df$year^2 + fit$coefficient[2]*df$year + fit$coefficient[1]

At last fit a quadratic curve:

plot(df$year,df$D, main="Heterogeineity across years", 
     xlab="Year ", ylab="D")
par(new = TRUE)
lines(df$year,quadratic, col="red")

Output:

Please note: We don't have your data.

Answer 2

A quadratic fit is quite straightforward in R using the linear model lm function with a quadratic term. The I() function (as is) is necessary to inhibit symbolic interpretation of the "^" operator and simplification the quadratic term. summary (or coef) print the coefficients and predict can be used to plot the curve:

## an example data set with 5 replicates
set.seed(123)
mydata <- data.frame(
  Year = rep(2007:2017, each=5),
  D = rep(c(56, 60, 64, 63, 65, 65, 64, 63, 64, 63, 62), each=5) + rnorm(55)
)

## fit a quadratic model
m <- lm(D ~ Year + I(Year^2), data = mydata)

summary(m)
coef(m)

plot(D ~ Year, data = mydata)
lines(mydata$Year, predict(m))

To do the same with plotmeans it is necessary to adjust the x scale.

library(gplots)
plotmeans(D ~ Year, main="Heterogeineity across years", data=mydata)

## plotmeans chances the x axis scale, so we
## need to subtract 2006, so that year 2007 is the first in plotmeans
lines(mydata$Year - 2007 + 1, predict(m), col="red")