Plotting Y=f(X) after a regression where X contains 2 predictors

I used

   mdl=fitlm(X,y)

to regress the y vector as a function of two predictors x1 and x2, which together form the X matrix.

I would like to obtain a plot of y=f(x1), with the data points, regression line and regression bands displayed. I know I can do all of this manually but I'm wondering if there's an easier way. I can see that plot(mdl) gives me an added variable plot with adjusted values, which in this case is not helpful, and I can see that there are no options to single out a single predictor for the plot - or is it the case that it would not make sense statistically to only plot y=f(x1) as long as there is an x2 predictor as well?

Thanks!

Answer 1

[Star Strider]

Does predict do what you want?

[AwedBy Matlab]

I don't think so, as that just seems to give me the y values of the regression line, so it would be the same as manually constructing the plot with the data points, regression line and confidence bands

[Star Strider]

You could plot f(x1) with your independent variable and some arbitrary single value for x2, but the error bars would likely not be meaningful, and I doubt you would get any meaningful information from the plot.

If you want to understand the effect of each parameter, your best option is to take the Jacobian of your function with respect to each parameter, [ df(x1,x2)/dx1 df(x1,x2)/dx2 ] where d here is understood to be the partial derivative.

Answer 2

[Ahmet Cecen]

It doesn't make sense to plot y vs f(x1). Here you have several options.

1) You can plot y vs x1 and y vs x2, which can show you how well each variable agrees with y. Cftool is an easy way to play around fits and scatter plots.

2) You can plot y vs x2 vs x1, which is another way to see how variables agree with y. (Cftool does this too)

3) You can plot y vs f(x1,x2) as a scatter plot, which is arguably the most meaningful thing you can plot.

There are a variety of diagnostic plots you can go for if your answer is unsatisfactory. I won't get into those here, check linear regression (assumptions) on wikipedia.

[AwedBy Matlab]

Sorry, I did in fact mean y vs x1 as the desired plot. I have several fitlm commands in my script, is there no way to use a handle from this command to achieve such y vs x1 plots in the script, as opposed to going into the Cftool GUI?

[Ahmet Cecen]

I am not aware of any such pre-loaded figure functions myself. The best I can suggest is to use a scatter() than a line() function and manually format the figure in the GUI. Afterwards you can go File-Generate Code, thus creating a function that can generate the figure instantly thereafter.

[AwedBy Matlab]

thanks Ahmet

Answer 3

[Tom Lane]

Have you considered the plotSlice function? It will plot predicted y vs. x1 for a fixed value of x2, and predicted y vs. x2 for a fixed value of x1.

[AwedBy Matlab]

I see, but does it also plot the regression line&bands, in addition to the individual data points?

[Tom Lane]

It plots the line and bands, but not the points unless there is just one predictor. That's because, for example, with two predictors a plot of f(x1,5) is not comparable to all the data points, only the points with x2=5.