Plotting curved confidence intervals for linear regression
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I am using coefCI function to estimate the confidence intervals of a linear model. I can plot this and get linear confidence bands for the regression line, but, I've seen plots of linear regression where the bands are curved. How can I get those? Thanks.
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Star Strider
2018-7-22
I did not see your post before.
Use the appropriate version of the predict (link) function for a compact linear model, predict (link) for a generalised linear model, or others, depending on what you are doing.
Those will give the confidence intervals. If you want to plot smooth curves, use:
xv = linspace(min(x), max(x), 1000);
for the independent variable ‘Xnew’ to use with predict.
8 个评论
Xen
2018-7-23
Star Strider
2018-7-23
My pleasure.
The confidence intervals do not need interpolation. Plot them as returned by predict.
If the confidence limits lines appear straight, that means there is not much variation in the confidence limits over the interval. This occurs if there is very little error in the dependent variable, especially with respect to its magnitude. (I opted for the 1000 points because I do not know your data set. That number should give a smooth approximation in any event. Change it as necessary.)
Without your data and relevant code, I cannot suggest any other reason for the confidence limit lines appearing not to vary over the limits of your independent variable. They should have a minimum difference at the mean of your independent variable, and a maximum (and approximately equivalent) difference at the extremes of your independent variable. Use that as a test to see if they are actually straight. (I suspect they are not.)
Xen
2018-7-25
Star Strider
2018-7-25
My pleasure.
They aren’t straight when I plot them, using essentially the same code as in my original Answer:
x = sort(rand(1,100));
y = rand(1,100);
mdl = fitlm(x,y);
Xnew = linspace(min(x), max(x), 1000)';
[ypred,yci] = predict(mdl, Xnew);
figure
plot(x, y, 'p')
hold on
plot(Xnew, ypred, '--g')
plot(Xnew, yci, '--r')
hold off
grid
Note that ‘Xnew’ must be a column vector.
Xen
2018-7-25
Star Strider
2018-7-25
Thank you.
If my Answer helped you solve your problem, please Accept it!
Prabhjot Dhami
2019-8-4
This answer appears to work great for a model with a single predictor.
However, when trying to use it with a model in which I have multiple predictors (e.g. 5), I get the following error:
Error using classreg.regr.CompactTermsRegression/designMatrix (line 166)
X must have 5 columns.
Error in LinearModel/predict (line 337)
design = designMatrix(model,Xpred);
Any idea as to how to plot confidence intervals from a fitlm structure based on a multiple linear regression model?
Chris Angeloni
2020-7-20
编辑：Chris Angeloni
2020-7-20
The short answer is that you get this error because you have multiple predictors, so the values in Xnew (or xv in the example above) should have a column for each predictor. (ie. you need to make an xv for every predictor in your multiple regression).
This makes visualizing the data tricky, because for every additional predictor, you add another dimension to your plot, I believe. The question here I think was focused mostly on linear regression with one predictor.
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