# Plotting plane from a matrix or data table

After weeks collecting data I've decided to pass my results through Wolfram Alpha and see what it gets. The results are amazingly useful, specially the plane generated by linear regression.

It is exactly what I want but the .nb and .cdf files generated (I've tried all available formats) are not editable.

My questions are: how can I achieve the same result using my Mathematica 10? Can I extract the plane equation?

EDIT:

Thanks for the comments and replies, guys. Here is a sample that is very similar to my data. Hope it is in the correct format (I'm a chemist and, in fact, I have used Mathematica just a few times, so, be patient).

{{"Theta", "Tau", "J"}, {78.65, 153.65, -1049.74}, {73.25,
154.4, -1317.43}, {74, 155.675, -1339.17}, {75.2,
154.15, -1265.85}, {77.1, 153.875, -1227.73}, {80.3,
153.325, -948.28}, {81.45, 153.05, -836.34}, {82.75,
152.95, -721.71}, {83.3, 152.875, -678.69}, {84.4,
152.625, -546.81}, {85.5, 152.525, -433.32}, {86.15,
152.4, -350.96}, {87.3, 152.25, -239.16}, {88.8,
151.9, -60.66}, {89.6, 151.75, 2.87}, {78.65,
115.575, -198.98}, {78.65, 118.775, -274.37}, {78.65,
122.075, -357.67}, {78.65, 125.525, -445.68}, {78.65,
129.1, -542.05}, {78.65, 132.775, -637.55}, {78.65,
136.625, -734.66}, {78.65, 140.65, -832.18}, {78.65,
144.825, -920.9}, {78.65, 149.075, -1002.04}, {78.65,
158.375, -1139.56}}

• Providing the data that cost your weeks to collect please. – yode Mar 14 '16 at 12:51
• Hi, @yode . I'm sorry for not providing the full data table but I'm not the main researcher behind this project. Despite not being any sensible information it is advised to not publish it before full validation. In this case, any practical example is of great help. – Henrique Junior Mar 14 '16 at 13:04
• Welcome to Mathematica.SE! I suggest the following: 0) Browse the common pitfalls question 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! – Dr. belisarius Mar 14 '16 at 13:55

point = Quiet@
RandomPoint[InfinitePlane[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}],
23] /. a_Real :> a + RandomReal[.1];
ListPlot3D[point]


Solve[a x + b y + c z + d == 0, z]


{{z -> (-d - a x - b y)/c}}

FindFit[point, (-d - a x - b y)/c, {a, b, c, d}, {x, y}] /.
Rule -> Set


{0.239107, -0.250077, 0.247355, -0.254698}

Plot3D[(-d - a x - b y)/c, {x, -1.29796, 1.29796}, {y, -1.29796,
1.29796}]


fakeData = Join @@ Table[{x, y, 3 x + 4 y + RandomReal[{-1, 1}]},
{x, -1, 1, .1}, {y, -1, 1, .1}];

lm = LinearModelFit[fakeData, {x, y}, {x, y}];

Show[ListPointPlot3D[fakeData, PlotStyle -> Red],
Plot3D[lm[x, y], {x, -1, 1}, {y, -1, 1}]]


• Maybe I have misunderstood the OP's English again. – yode Mar 14 '16 at 14:00
• @yode Or perhaps I did. Who knows? :) – Dr. belisarius Mar 14 '16 at 14:01