How to fit a polynomial curve ?

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# We create 2 vectors x and y x <- runif(300, min=-10, max=10) y <- 0.1*x^3 - 0.5 * x^2 - x + 10 + rnorm(length(x),0,8) # plot of x and y : plot(x,y,col=rgb(0.4,0.4,0.8,0.6),pch=16 , cex=1.3) # 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 add it to the current plot ! myPredict <- predict( model ) ix <- sort(x,index.return=T)$ix lines(x[ix], myPredict[ix], col=2, lwd=2 ) # I add the features of the model to the plot coeff=round(model$coefficients , 2) text(3,-70 , paste("Model : ",coeff[1] , " + " , coeff[2] , "*x" , "+" , coeff[3] , "*x^2" , "+" , coeff[4] , "*x^3" , "\n\n" , "P-value adjusted = ",round(summary(model)$adj.r.squared,2))) |

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As far as I know, the p-value is not the same as the r-squared ! In the text the r-squared is plotted and titeld as p-value.