Tukukkk

In the below Manipulate expression:

Discretize=Function[{f,steps,x1},Table[f[x],{x,0,x1,Floor[x1/steps]}]];

MakePoints=Function[var,Table[x^2+RandomReal[{-var,var}],{x,0,15,1}]];

Manipulate[

 GetDiff = Function[

   Total[dta] - Total[mdl]

   ];

 dta = MakePoints[15];

 mdl = Discretize[Function[x, τ*x^2], Length[dta] - 1, 

   Length[dta] - 1];

 ListLinePlot[{dta, mdl}, 

  PlotRange -> {{0, Length[dta] - 1}, {0, 250}}, 

  PlotLegends -> {"data", "model"}],

 {{τ, 1}, .01, 3, .01},

 Dynamic[

  diff = GetDiff;

  "τ: " <> ToString[τ] <>

   "nΣdata: " <> ToString[Total[dta]] <>

   "nΣmodel: " <> ToString[Total[mdl]] <>

   "nΣdata-Σmodel: " <> ToString[diff]

  ]

 ]

Why does varying the parameter seemingly reevaluate dta? I get a constantly changing dta line while I vary the parameter.

Your MakePoints[ ] function has a RandomReal[ ] function call in it, so it is randomizing each time you move the Manipulate slider. Just move it outside.

dta = MakePoints[15];



Manipulate[GetDiff = Function[Total[dta] - Total[mdl]];

 (*dta=MakePoints[15];*)

 ...Etc.]

or you can wrap the internal random call with a BlockRandom[ ]

Manipulate[GetDiff = Function[Total[dta] - Total[mdl]];

     dta = BlockRandom@MakePoints[15];

    .... Etc. ]

Your code can be fixed and made much simpler and more efficient, all at the same time. Like so;

Discretize = Function[{f, steps, x1}, Table[f[x], {x, 0, x1, Floor[x1/steps]}]];



MakePoints = Function[var, Table[x^2 + RandomReal[{-var, var}], {x, 0, 15, 1}]];



SeedRandom[1];

Manipulate[

  mdl = Discretize[Function[x, τ x^2], Length[dta] - 1, Length[dta] - 1];

  tmdl = Total[mdl];

  Column[{

     ListLinePlot[{dta, mdl},

       PlotRange -> {{0, Length[dta] - 1}, {0, 250}}, 

       PlotLegends -> {"data", "model"},

       ImageSize -> Medium],

     Row[{"Σdata: ", tdta}],

     Row[{"Σmodel: ", tmdl}],

     Row[{"Σdata-Σmodel: ", tdta - tmdl}]}],

  {{dta, MakePoints[15]}, None},

  {{tdta, Total[dta]}, None},

  {mdl, None},

  {tmdl, None},

  {{τ, 1}, .01, 3, .01, Appearance -> "Labeled"},

  TrackedSymbols :> {τ}]]

Notes

1. 
   GetDiff is not needed.


2. Introducing some local variables with specifications of the form {varspec, None}, which are automatically dynamic, makes for cleaner code and makes it easy to set static values for data and tdta.


3. Calling MakePoints as an initializer in the specification of dta fixes you problem of unwanted re-evaluation.


4. Only τ need be tracked, which reduces the load on the front-end.


5. Introducing Column and Row much simplifies the formatting of the output.


6. Adding the Appearance -> "Labeled" option to the specification of τ eliminates the need to write code to show τ in the output,


7. This approach does not require calling Dynamic explicitly anywhere in the Manipulate expression.

Another option using DynamicModule which is the proper tool for interfaces that have local variables:

DynamicModule[

 {MakePoints, Discretize, dta, tdta, mdl, tmdl},

 Manipulate[

  mdl = Discretize[Function[x, τ x^2], Length[dta] - 1, 

    Length[dta] - 1];

  tmdl = Total[mdl];

  Grid[

   {

    {

     ListLinePlot[

      {dta, mdl},

      PlotRange -> {{0, Length[dta] - 1}, {All, 250}},

      PlotLegends -> {"data", "model"}, ImageSize -> Medium

      ],

     SpanFromLeft

     },

    {Subscript["Σ", "data"], ":", tdta},

    {Subscript["Σ", "model"], ":", tmdl},

    {

     Row@{Subscript["Σ", "data"], "-", 

       Subscript["Σ", "model"]}, ":",

     tdta - tmdl

     }

    },

   Alignment -> Left

   ],

  {{τ, 1}, .01, 3, .01, Appearance -> "Labeled"},

  TrackedSymbols :> {τ}

  ],

 Initialization :> {

   MakePoints = 

    Function[var, Range[0, 15]^2 + RandomReal[{-var, var}, 16]], 

   Discretize = 

    Function[{f, steps, x1}, Table[f[x], {x, 0, x1, Floor[x1/steps]}]],

   dta = MakePoints[15],

   tdta = Total[dta]

   }

 ]