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

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AwedBy Matlab on 1 Aug 2014
Commented: Tom Lane on 14 Aug 2014
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!

Star Strider on 1 Aug 2014
Does predict do what you want?
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Star Strider on 1 Aug 2014
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.

Ahmet Cecen on 1 Aug 2014
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 on 2 Aug 2014
thanks Ahmet

Tom Lane on 8 Aug 2014
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.
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Tom Lane on 14 Aug 2014
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.

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