Multiple Linear Regression - obtaining equation with constant term

Question

I am trying to use the LinearModelFit function to obtain a linear regression of my 5 inputs for my single output. I have the input data:

    MasterDataInputs={{"payload", "travel_empty_time", "travel_loaded_time", 
  "net_loaded_lift", "idle_time"}, {16241., 89126., 81075., 7747., 
  84323.}, {2364., 10879., 10811., 1421., 12708.}, {4297., 22730., 
  24092., 373., 16606.}, {5494., 30667., 32297., 999., 
  20341.}, {3926., 22025., 20520., 3410., 23993.}, {6193., 31027., 
  28319., 4948., 30262.}, {5709., 27699., 25351., 1990., 
  26282.}, {2178., 13410., 14036., 1433., 12485.}, {3605., 18509., 
  17690., 2238., 12170.}, {5620., 28632., 24355., 3538., 
  27632.}, {4352., 25259., 28307., 2176., 16712.}, {12550., 59921., 
  59001., 3095., 58977.}, {5520., 30586., 26967., 4121., 
  17851.}, {3193., 19732., 19310., 2769., 15507.}, {9732., 56096., 
  57320., 8088., 45418.}, {4531., 23906., 30182., 3789., 
  18930.}, {4521., 27455., 26796., 3356., 21291.}, {4286., 25317., 
  27807., 2777., 15309.}, {4226., 24740., 31243., 3056., 
  20926.}, {3060., 20052., 22617., 2144., 12753.}, {4738., 28425., 
  24036., 4534., 24927.}, {7900., 46413., 47040., 4764., 
  37522.}, {6964., 41928., 36873., 3729., 32866.}, {19063., 99629., 
  102567., 4959., 70360.}, {5043., 30703., 28573., 2819., 
  23747.}, {8070., 43767., 41004., 2281., 33673.}, {4580., 25321., 
  25370., 2562., 21293.}, {7012., 47499., 38037., 6957., 
  35961.}, {1616., 8119., 7718., -18., 6468.}, {2853., 16548., 16089.,
   2572., 12738.}, {13729., 94984., 83507., 7410., 71171.}, {5644., 
  33104., 36720., 3420., 31578.}, {8280., 57066., 49212., 4818., 
  38604.}, {5620., 34289., 30598., 3970., 26980.}, {5881., 35405., 
  37019., 4177., 34324.}, {3364., 21765., 20473., 2613., 
  13166.}, {5174., 31533., 29321., 4872., 27182.}, {5435., 35767., 
  31029., 3773., 31672.}, {5880., 39594., 33352., 6140., 
  35198.}, {3814., 23659., 26286., 2724., 18484.}, {1271., 7350., 
  7163., 1319., 9607.}, {9463., 60296., 63248., 9054., 
  45353.}, {3243., 22832., 25124., 3451., 15275.}, {8022., 48725., 
  48224., 8829., 38922.}, {1805., 11246., 12426., 687., 9147.}}

and the outputs:

MasterDataOutput ={"fuel output", 2099.749899, 1384.120668, 1620.060306, 1755.348166, \
1595.189198, 1798.31186, 1722.579319, 1411.483751, 1537.460621, \
1730.932625, 1671.089154, 2010.22954, 1760.840169, 1536.90848, \
2126.08609, 1691.889546, 1688.623823, 1670.48431, 1681.022846, \
1549.985641, 1695.898173, 1979.419182, 1897.569649, 2280.36639, \
1732.712557, 1933.740813, 1666.700071, 1966.088623, 1304.244403, \
1480.054095, 2105.763533, 1799.491245, 2029.785039, 1793.720838, \
1825.476258, 1563.436693, 1761.070177, 1785.978395, 1854.485829, \
1628.997857, 1281.707381, 2152.698111, 1595.443235, 2061.991531, \
1366.867529}

I have tried the following after searching this forum and the help:

LinearModelFit[{MasterDataInputs[[2 ;;]], MasterDataOutput[[2 ;;]]}, 
  MasterDataInputs[[1]]] 

which resulted in an equation without a constant. I need a constant in my equation so I tried:

LinearModelFit[{MasterDataInputs[[2 ;;]], MasterDataOutput[[2 ;;]]}, 
  MasterDataInputs[[1]], IncludeConstantBasis -> True] // Normal

which still gives me no constant even though the help says it should. I have also tried the below:

LinearModelFit[{MasterDataInputs[[2 ;;]], MasterDataOutput[[2 ;;]]}, 
  IncludeConstantBasis -> True] // Normal

and all variation without the //Normal at the end. Please will someone help, I need a linear regression equation with a constant term.

Answer 1

I prefer the more general function; you can do :

data = Transpose[
   Join[Transpose[
     MasterDataInputs[[2 ;;]]], {MasterDataOutput[[2 ;;]]}]][[1 ;; 2]] ;

nlm = NonlinearModelFit[data, 
  a0 + a1 x1 + a2 x2 + a3 x3 + a4 x4 + a5 x5, {a0, a1, a2, a3, a4, 
   a5}, {x1, x2, x3, x4, x5}]

nlm // Normal
(* 1254.18 +0.0102011 x1+0.00115933 x2+0.00164517 x3+0.0340745 x4+0.00212529 x5 *)