45-confidence-interval-around-polynomial-curve-fitting.Rmd

---
title: "Polynomial curve fitting and confidence interval"
descriptionMeta: "Build a scatterplot with a polynomial curve and its confidence interval drawn on top of it. Base R code provided."
descriptionTop: "This example follows the previous [scatterplot with polynomial curve](44-polynomial-curve-fitting.html). It extends this example, adding a confidence interval."
sectionText: "Scatter section"
sectionLink: "scatterplot.html"
DataToVizText: "Data to Viz"
DataToVizLink: "data-to-viz.com/graph/scatter.html"
url: "45-confidence-interval-around-polynomial-curve-fitting"
output:
  html_document:
      self_contained: false    
      mathjax: default
      lib_dir: libs
      template: template_rgg.html
      css: style.css
      toc: TRUE
      toc_float: TRUE
      toc_depth: 2
      df_print: "paged"
---


```{r global options, include = FALSE}
knitr::opts_chunk$set( warning=FALSE, message=FALSE)
```

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This example follows the previous [chart #44](44-polynomial-curve-fitting.html) that explained how to add polynomial curve on top of a [scatterplot](scatterplot.html) in base R.  

Here, a confidence interval is added using the `polygon()` function.
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```{r thecode, echo=FALSE, out.width = "100%", fig.height=7}
# We create 2 vectors x and y. It is a polynomial function.
x <- runif(300, min=-30, max=30) 
y <- -1.2*x^3 + 1.1 * x^2 - x + 10 + rnorm(length(x),0,100*abs(x)) 

# Basic plot of x and y :
plot(x,y,col=rgb(0.4,0.4,0.8,0.6), pch=16 , cex=1.3 , xlab="" , ylab="") 

# Can we find a polynome that fit this function ?
model <- lm(y ~ x + I(x^2) + I(x^3))

# I can get the features of this model :
#summary(model)
#model$coefficients
#summary(model)$adj.r.squared

#For each value of x, I can get the value of y estimated by the model, and the confidence interval around this value.
myPredict <- predict( model , interval="predict" )

#Finally, I can add it to the plot using the line and the polygon function with transparency.
ix <- sort(x,index.return=T)$ix
lines(x[ix], myPredict[ix , 1], col=2, lwd=2 )
polygon(c(rev(x[ix]), x[ix]), c(rev(myPredict[ ix,3]), myPredict[ ix,2]), col = rgb(0.7,0.7,0.7,0.4) , border = NA)
```
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```{r thecode, eval=FALSE}
```









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```{r, echo=FALSE}
htmltools::includeHTML("htmlChunkRelatedCorrelation.html")
```