toshiakit/95_confidence_intervals

Plotting shaded 95% Confidence Intervals

Created with R2022b. Compatible with R2021b and later releases

I saw a Reddit post that asked:

Hello! I am having trouble plotting my confidence intervals. Ideally I want to create a figure that looks like this where the mean is the solid line and the shaded region is the confidence intervals

Let's give it a try.

We start with making up randomly generate data to play with. I am using integer for this, because it will make it easier to see what's going on later.

x = randi(100,[100,1]);
n = randn(100,1)*5;
y = 2*x + n;

We can the use Curve Fitting Toolbox to fit a curve, and plot it with confidence intervals. In this case, the confidence intervals are between two dotted lines.

f = fit(x,y,'poly1');
figure
plot(f,x,y,'PredObs')

And there is the output (Fig1)

This is simple enough, but the OP wanted to use shaded intervals, like this one.

You can use predint to get confidence intervals.

ci = predint(f,x); 

And this should match exactly the confidence interval lines from Fig1.

figure
plot(x, ci)
hold on
plot(f,x,y)

Now, we can use this to create a shaded area using fill, as shown in the documentation linked above.

One thing we need to understand is that fill expects vectors of x and y as input that define points in a polygon. So x should be lined up in such as way that define the points on x-axis that maps to the points in a polygon in the order that segments that form the polygon should line up.

That's not the case with the raw data we have, x. Therefore we need to generate a new x that orders the points in a sequence based on how the polygon should be drawn.

Our x ranges from 1 to 100 and has 100 elements, so we can define a new xconf that lines up the data in a sequence, and generate confidence intervals based on xconf.

xconf = (1:100)';
ci = predint(f,xconf);

However, this only defines one of the segments of the polygon from 1 to 100. We need another segment that covers the points from 100 to 1.

xconf = [xconf; xconf(100:-1:1)];

And ci already has two segments defined in two columns, so we just need to turn it into a vector by concatenating two columns.

yconf = [ci(:,1); ci(100:-1:1,2)];

Let's now plot the polygon.

figure
p = fill(xconf,yconf,'red');

xconf and yconf correctly define the polygon we need. Now all we need to do is to overlay the actual data and make it look nicer.

p.FaceColor = [1 0.8 0.8];      
p.EdgeColor = 'none';
hold on
plot(f,x,y)

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