Plane of best fit (without using the sftool)

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kanai
kanai 2013-7-31
I would like to to know the equation of a plane of best fit using a set of 20 xyz coordinates. I can do it using the SF tool but I would like to know the code to run for my data to get it in the command bar and without using the cumbersome SFtool
Once I have the equation I would like to find the point on the plane where a line crosses it. This line would be in a parametric format.
Many thanks kg

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回答（1 个）

Tom Lane
Tom Lane 2013-8-1
If you set up a matrix X with three columns containing your x values, your y values, and a column of twenty ones, and set up a Y column vector containing your z values, then
b = X\y
will return the least-squares coefficient estimates. This is the least squares solution in the sense of minimizing the errors in the z direction.
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Tom Lane
Tom Lane 2013-8-3
If you have x,y,z as column vectors of the same length, then
b = [ones(size(x)),x,y]\z
will estimate three coefficients for predicting z: the intercept, the multiplier of x, and the multiplier of y.
kanai
kanai 2013-8-15
Apologies but that has not worked for me
b=x\y gives me a number (-17.3271)
Can you give me any further help? Also once I have an equation of a plane (for the moment I will use the plane calculated by the sftool), say it is x+y+z=0, how to I plot this?
Many thanks

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