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I have been trying for a while plotting a polynomial regression using R. I have read several libraries, as ggplot2, qplot, etc, with no succeed. The next are my data:

I normally use the R GUI called R commander. Is there any option to get this plot without writing commands directly in the prompt line by using this GUI?

X   Y
97.6470588235   5.98290598291
92.9411764706   14.5299145299
90,00   22.2222222222
85.2941176471   29.9145299145
80,00   37.6068376068
74.1176470588   46.1538461538
68.8235294118   52.9914529915
64.1176470588   58.9743589744
58.2352941176   64.9572649573
52.3529411765   70.9401709402
47.0588235294   76.0683760684
41.7647058824   81.1965811966
36.4705882353   84.6153846154
31.1764705882   88.8888888889
25.8823529412   92.3076923077
19.4117647059   95.7264957265
77.6470588235   41.0256410256
83.5294117647   33.3333333333
96.4705882353   9.40170940171
88.8235294118   24.7863247863
100,00  0,00
96.186440678    7.27272727273
91.9491525424   15.7575757576
88.9830508475   21.8181818182
85.1694915254   28.4848484848
80.9322033898   36.3636363636
78.813559322    39.3939393939
74.5762711864   46.0606060606
70.3389830508   52.1212121212
64.406779661    61.2121212121
56.7796610169   70.303030303
49.5762711864   78.1818181818
42.7966101695   84.8484848485
36.8644067797   89.696969697
31.7796610169   93.3333333333
26.2711864407   97.5757575758
21.186440678    100,00
61.4406779661   64.8484848485
68.2203389831   55.7575757576
53.813559322    73.3333333333

I obtained its quadratic regression and the coefficients for the confidence intervals:

Call:
lm(formula = Y ~ X + I(X^2), data = Datos2)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2599 -1.3415  0.1541  1.3610  3.2911 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.013e+02  1.971e+00  51.419   <2e-16 ***
X           -8.086e-03  7.069e-02  -0.114     0.91    
I(X^2)      -9.886e-03  5.727e-04 -17.263   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.824 on 37 degrees of freedom
Multiple R-squared:  0.9964,    Adjusted R-squared:  0.9962 
F-statistic:  5132 on 2 and 37 DF,  p-value: < 2.2e-16


> Confint(LinearModel.3, level=0.95)
                 Estimate       2.5 %        97.5 %
(Intercept) 101.323700913 97.33098252 105.316419306
X            -0.008086099 -0.15131294   0.135140742
I(X^2)       -0.009885921 -0.01104624  -0.008725598

However, trying to plot the quadratic regression and its Confidence intervals resulted in a more than expected hard work.

Which could be the correct command (or route using R commander) to get a professional plot view? I tried several ggplot and qplot with no succeed.

On the other hand, substituting particular X values in those three equations I get something which may be wrong. I mean. On the left side, the confidence interval must be wider than on the right side. However, what I see is the contrary, narrower the left and wider the right. A quick plot using LibreOffice Calc showing this: enter image description here The distance between the red and blue lines (95%CI) must be narrower on the right side than on the left side.

Thanks in advance for your comments. Mario

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  • $\begingroup$ Could you elaborate on why you think the distance must be narrower on the right side (larger independent values) than on the left? And what "three equations" did you substitute the x values into? $\endgroup$
    – whuber ♦
    Commented Jan 30, 2015 at 19:44
  • $\begingroup$ Plot the original data and you will see that it is unlikely that the right side would be wider than the left side. Ohterwise, when I plot the raw data using other statistical software (PAST), the confidence interval which appears is exactly in the same way as I am describing. $\endgroup$
    – antecessor
    Commented Feb 1, 2015 at 9:29
  • $\begingroup$ The original data tell you nothing about the relative widths of confidence bands at different locations, because they are not computed locally: they summarize all the data. The second part of your comment is important: it suggests you are not correctly computing the confidence bands at all. Unfortunately, you haven't really indicated how you are computing them, making it impossible to suggest what exactly is wrong. $\endgroup$
    – whuber ♦
    Commented Feb 1, 2015 at 14:42
  • $\begingroup$ Thanks whuber for your comment. I want a plot where the quadratic regression is represented and also its confidence interval (at 95%). I did it with other software but I want to do it with R, and learning howto do it. $\endgroup$
    – antecessor
    Commented Feb 2, 2015 at 8:00

1 Answer 1

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This StackOverflow question on plotting confidence intervals may help you with the R code.

I think a base point of confusion is that the confidence interval limits for a quadratic fit are not themselves quadratics. The interval limits need separate evaluation. Here's a plot made with different software. The data fits so well, I had to crank the alpha level down to 0.001 to get any sense of the confidence interval.

enter image description here

Using a small subset of the data shows the phenomenon better:

enter image description here

Separately of interest: as you can sort of tell from the original data plot and you can strongly tell from the residuals plot, there seems to be something else going on, such as two interleaved functions selected by some hidden variable.

enter image description here

Guessing at the two populations gives two even stronger looking fits, at least for the left side:

enter image description here

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