;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Variable declarations ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;

globals
[
  shape-names  ;; list that holds the names of the shapes a student's turtle can have
  m  ;; the slope of the line of regression- only calculated if linear-regression? is true
  b  ;; the y-intersept of the line of regression- only calculated if linear-regression? is true
  r-square  ;; the correlation coefficient of the line of regression- only calculated if linear-regression? is true
  equation  ;; the equation for the line of regression- only calculated if linear-regression? is true
  challenge  ;; holds the current verbal challenge that the instructor gives to the users

;; quick start instructions variables
  quick-start  ;; the current quickstart instruction displayed in the quickstart monitor
  qs-item  ;; the index of the current quickstart instruction
  qs-items  ;; the list of quickstart instructions
]

turtles-own
[
  user-id  ;; unique id generated by each calculator to identify each student or teacher turtle
]

patches-own
[
  axis?  ;; true if the pxcor or pycor are 0
  reg-point?  ;; true if the patch falls on the line of regression
]


;;;;;;;;;;;;;;;;;;;;;
;; Setup Functions ;;
;;;;;;;;;;;;;;;;;;;;;

to startup
  setup-quick-start
  hubnet-set-client-interface "TI-83+" [ "AAA - Function Activity 2.4" [ "L1" ] ]
  hubnet-reset
  setup
end

;; Initializes the display, and creates a list that contains the names of the shapes
;; used by turtles in this activity.  The placement of the shape names in the last
;; corresponds to the numbers sent by calculators.
to setup
  cc
  cp
  ct
  clear-all-plots

  ;; setup and draw the axes
  ask patches
  [
    ifelse (pxcor = 0 or pycor = 0)
    [
      set pcolor 2
      set axis? true
    ]
    [
      set pcolor 0
      set axis? false
    ]
  ]

  ;; create a list of the shape names for the calculators to use
  set shape-names ["wide wedge" "square" "" "thin wedge" "" "" "" "car"]

  ;; initialize the equation for the line of regression to be nothing
  set equation ""

  ;; initially set the challenge to nothing
  set challenge ""
    
  ;; send the appropriate setup information to the calculators
  setup-hubnet
end

;; give the user some information about what the setup button does so they can 
;; know whether they want to proceed before actually doing the setup
to setup-prompt
  if user-yes-or-no? ("The SETUP button should only be used when starting "
              + "over with a new group (such as a new set of students) since "
              + "all data is lost.  Use the RE-RUN button for continuing with "
              + "an existing group."
              + "\n\nDo you really want to setup the model?")
  [
    user-message "Before closing this dialog, please do the following:"
                 + "\n  -Have everyone that is currently logged in, log off and "
                 + "clear the calulator memory. (Press 2nd MEM 7 1 2)"
                 + "\n  -Open the teacher console for this activity and press the ERASE ALL DATA button."
    setup
  ]
end

;; only used in testing- creates some turtles to test the activity
to make-test-turtles [ num ]
  cct num
  [
    set heading 0
    setxy random-float screen-size-x random-float screen-size-y
    set user-id -1
  ]
end


;;;;;;;;;;;;;;;;;;;;;;;
;; Runtime Functions ;;
;;;;;;;;;;;;;;;;;;;;;;;

;; receives information from the calculators and runs the simulation
to go
  ;; set all patches to have be not patches on the line of regression
  ask patches
  [ set reg-point? false ]

  ;; get any new information from the calculators
  listen-calc

  ;; do the calculations for determining the equation of the line of regression and correlation coefficient
  if linear-regression?
  [ lin-reg ]

  ;; remove or draw the line of regression for all patches that have reg-point? true
  ask patches
  [
    ;; draw the line of regression.  note: reg-point? can only ever be true if linear-regression? is true
    ifelse reg-point?
    [ set pcolor 13 ]
    [
      ;; draw the axes or the background to an appropriate color
      ifelse axis?
      [ set pcolor 2 ]
      [ set pcolor black ]
    ]
  ]
end

to lin-reg
  locals
  [
    ave-x  ;; the average of all the turtles' xcors
    ave-y  ;; the average of all the turtles' ycors
    sum-x  ;; the sum of all the turtles' xcors
    sum-y  ;; the sum of all the turtles' ycors
    sum-xy  ;; the sum of the product of each turtle's xcor and ycor
    sum-x-square  ;; the sum of the product of each turtle's xcor squared
    sum-y-square  ;; the sum of the product of each turtle's ycor squared
    num-turtles  ;; the number of turtles
    denominator  ;; holds the denominator for the calculations of the slope and the y-intersept
    xcors  ;; a list containing the xcors of the turtles
    ycors  ;; a list containing the ycors of the turtles
  ]

  ;; you need to have at least two points to make a line
  if count patches with [ any? turtles-here ] > 1
  [
    ;; initialize the variables
    set num-turtles count turtles
    set xcors values-from turtles [ xcor ]
    set ycors values-from turtles [ ycor ]
    set sum-x sum xcors
    set sum-y sum ycors
    set ave-x sum-x / num-turtles
    set ave-y sum-y / num-turtles
    set sum-xy sum values-from turtles [ xcor * ycor ]
    set sum-x-square sum values-from turtles [ xcor * xcor ]
    set sum-y-square sum values-from turtles [ ycor * ycor ]

    ;; compute and store the demonimator for the slope and y-intercept so we don't have to do it twice
    set denominator ( sum-x-square - num-turtles * ( ave-x ^ 2 ) )

    ;; if the denominator = 0 or the min of xcors = the max of xcors, the turtles are in a vertical line
    ;; thus, the line of regression will be undefined and have a r^2 value of 1.0
    ifelse ( denominator = 0 ) or ( min xcors = max xcors )
    [
      set m 0
      set b 0
      set equation "Undefined"
      ;; since all the turtles are in a line r^2 must be 1
      set r-square 1
      ;; set all the patches in the column to be on the line
      ask patches with [ pxcor = xcor-of one-of turtles ]
      [ set reg-point? true ]
    ]
    [
      ;; otherwise, we have some other type of line.  so find the y-intersept and slope of the line
      set b ( ( ave-y * sum-x-square ) - ( ave-x * sum-xy ) ) / denominator
      set m ( sum-xy - num-turtles * ave-x * ave-y ) / denominator

      ;; set the equation to the appropriate string
      set equation ( precision m 2 ) + "X + " + ( precision b 2 )

      ;; compute the value of r^2
      ifelse ( ( sum-y-square - num-turtles * ( ave-y ^ 2 ) ) = 0 ) or ( min ycors = max ycors )
      [ set r-square 1 ]
      [
        set r-square ( ( sum-xy - num-turtles * ave-x * ave-y ) ^ 2 ) /
          ( ( sum-x-square - num-turtles * ( ave-x ^ 2 ) ) * ( sum-y-square - num-turtles * ( ave-y ^ 2 ) ) )
      ]

      ;; set the patches' reg-point? to true if they lie on the line of regression
      ask patches with [ pycor = round ( m * pxcor + b ) ]
      [ set reg-point? true ]
    ]
  ]
end

;; sets challenge to the value that the user enters in an input dialog
to set-challenge
  set challenge user-input "Enter the Verbal Challenge:"
end


;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Quick Start functions ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; initialize instructions to quickly setup the model, calculators, and TISchool webpage to run this activity
to setup-quick-start
  set qs-item 0
  set qs-items
  [
    "Teacher: Follow these directions to setup the HubNet activity."
    "Optional- Zoom In (see Tools in the Menu Bar) - optional"
    "Press the GO button."
    "Everyone: Reset the RAM on your calculator (2nd MEM 7 1 2)."
    "Login to the calculator."
    "Choose the PICK POINTS option."
    "Remember your shape and color and press ENTER."
    "Move around using the arrow keys to..." "acquaint yourselves with the interface."
    "Teacher: Issue your students a challenge, such as..." "create a mock data set with an R^2 of .75."
    "Optional- Press the NetLogo SET CHALLENGE button and enter..." "the challenge to be displayed in the CURRENT CHALLENGE monitor."
    
    "Teacher: To rerun the activity, do not clear the server."
    "Stop the simulation by pressing the NetLogo GO button."
    "Press the NetLogo RE-RUN button."
    "Press the GO button."
    "Everyone: Exit to the calculator Main Menu."
    "Choose the RESTART option from the calculator Main Menu."
    "Choose the PICK POINTS option and continue."
    
    "Teacher: To start the simulation over with a new group,..." "stop the model by pressing the NetLogo GO button, if it is on."
    "Have everyone, including yourself, logout of their calculators."
    "Press the ERASE ALL DATA button on the TISCHOOL site."
    "Press the NetLogo SETUP button."
    "Follow these instructions from the beginning again."
  ]
  set quick-start item qs-item qs-items
end

;; view the next item in the quickstart monitor
to view-next
  set qs-item qs-item + 1
  if qs-item >= length qs-items
  [ set qs-item length qs-items - 1 ]
  set quick-start item qs-item qs-items
end

;; view the previous item in the quickstart monitor
to view-prev
  set qs-item qs-item - 1
  if qs-item < 0
  [ set qs-item 0 ]
  set quick-start item qs-item qs-items
end


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Code for interacting with the calculators ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; send the appropriate setup information to the calculators
to setup-hubnet
  locals
  [
    parameters  ;; the setup information to be sent to the calculators
  ]
  
  set parameters [ 1 ]  ;; 1 means that we can only have one point on the calculators
  set parameters lput (- screen-edge-x) parameters  ;; append the negative screen-edge-x
  set parameters lput screen-edge-x parameters  ;; append the screen-edge-x
  set parameters lput (- screen-edge-y) parameters  ;; append the negative screen-edge-y
  set parameters lput screen-edge-y parameters  ;; append the screen-edge-y

  hubnet-broadcast "PARAM" parameters
end

;; when a command is sent, this finds out which calculator sent it and then executes the command
to listen-calc
  locals
  [
    current-id
    cmd
  ]

  while [ hubnet-message-waiting? ]
  [
    hubnet-fetch-message
    set current-id hubnet-message-source
    set cmd item 0 hubnet-message
    execute-cmd current-id cmd
  ]
end

to execute-cmd [ current-id cmd ]
  if cmd = 0
  [ exe-crt current-id ]
  if cmd = 3
  [ exe-kill current-id ]
end

; 0 Create or Move current Turtles - receives a list 6 items long - 1, shape, color, x, y, and point number (this is unused)
to exe-crt [ current-id ]
  ifelse not any? turtles with [ user-id = current-id ]
  [
    cct item 1 hubnet-message
    [
      set user-id current-id
      set heading 0
      set shape item (item 2 hubnet-message) shape-names
      set color (item 3 hubnet-message)
      setxy (item 4 hubnet-message) (item 5 hubnet-message)
    ]
  ]
  [
    ask turtles with [ user-id = current-id ]
    [ setxy (item 4 hubnet-message) (item 5 hubnet-message) ]
  ]
end

;3 Kill Turtles - kills turtle associated with id current-id
to exe-kill [ current-id ]
  ask turtles with [ user-id = current-id ]
  [ die ]
end


; ***NetLogo Model Copyright Notice***

; This activity and associated models and materials was created as part of the project:
; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS.
; The project gratefully acknowledges the support of the 
; National Science Foundation ( REPP program ) -- grant number REC #9814682.

; Copyright 2000 by Uri Wilensky & Walter Stroup. Updated 2001,2002. All rights reserved.

; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from the copyright holders.
; Contact the copyright holders for appropriate licenses for redistribution for
; profit.

; To refer to this model in academic publications, please use:
; Wilensky, U. & Stroup, W. (2000).  NetLogo HubNet Regression model.
; http://ccl.northwestern.edu/netlogo/models/HubNetRegression.
; Center for Connected Learning and Computer-Based Modeling,
; Northwestern University, Evanston, IL.

; In other publications, please use:
; Copyright 1998 by Uri Wilensky and Walter Stroup.  All rights reserved.  See
; http://ccl.northwestern.edu/netlogo/models/HubNetRegression
; for terms of use.
;
; ***NetLogo Model Copyright Notice***
@#$#@#$#@
GRAPHICS-WINDOW
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520
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15
11.0
1
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1
1

CC-WINDOW
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Command Center

BUTTON
3
10
68
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Setup
setup-prompt
NIL
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T
OBSERVER
T

BUTTON
170
60
235
93
Go
go
T
1
T
OBSERVER
T

MONITOR
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283
Mouse X
(round mouse-xcor)
1
1

MONITOR
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Mouse Y
(round mouse-ycor)
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MONITOR
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Quick Start Instructions (more details in info tab)
quick-start
0
1

BUTTON
461
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539
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<<< PREV
view-prev
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OBSERVER
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BUTTON
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NEXT >>>
view-next
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OBSERVER
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BUTTON
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60
406
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Reset Instructions
setup-quick-start
NIL
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OBSERVER
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MONITOR
2
179
177
228
Number of Points at Mouse
count turtles-at round mouse-xcor round mouse-ycor
0
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SWITCH
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linear-regression?
linear-regression?
0
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MONITOR
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R^2
r-square
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MONITOR
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Equation
equation
3
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MONITOR
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Current Challenge
challenge
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BUTTON
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Set Challenge
set-challenge
NIL
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OBSERVER
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BUTTON
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Re-Run
setup
NIL
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OBSERVER
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@#$#@#$#@
WHAT IS IT?
-----------
This model is used for an introductory approach to regressions.  Linear Regression is the fitting of a straight line through a given set of points.  Most commonly, the best-fit line is used.  The best-fit line is the line that has the highest R^2 value for this set of points.  R^2 is known as the correlation coefficient.  This value indicates how well the line of regression fits the data on a scale from 0 to 1.  The closer R^2 is to 1, the closer the line fits the data.

In this model however, you will create a set of points to create a line of regression that will have a specific R^2 value.  Issue your students a challenge, such as create a mock data set with an R^2 of .5 and then of .8.  How did the data change?  Try to data sets that have different slopes or y-intercepts.

This activity requires the TI Navigator activity AAA - Function Activity 2.4

For further documentation, see the Participatory Simulations Guide found at http://ccl.northwestern.edu/ps/


HOW TO USE IT
-------------

QUICKSTART INSTRUCTIONS:
------------------------
Contains instructions as to how to quickly setup the model, calculators, and TISchool web page so as to run this activity.  The instructions can be found below:

Teacher: Open the TISchool site in your web browser.
Enable activity AAA - Function Activity 2.4.
Open the teacher console and press the ERASE ALL DATA button.

If it is not open already, open the NetLogo model.
If you are prompted by a Login dialog, enter your teacher id and password and any other necessary information.
Optional- Zoom In (see Tools in the Menu Bar)
Press the GO button.

Everyone: Reset the RAM on the calculator by pressing the following keys: 2nd MEM 7 1 2.
Login to the calculator.
Choose the PICK POINTS option.
Remember your shape and color and press ENTER.
Move around using the arrow keys to acquaint yourselves with the interface.

Teacher: Issue your students a challenge, such as create a mock data set with an R^2 of .75.
Optional- Press the NetLogo SET CHALLENGE button and enter the challenge to be displayed in the CURRENT CHALLENGE monitor.

Teacher: To rerun the activity, do not clear the server.
Stop the simulation by pressing the NetLogo GO button.
Press the NetLogo RE-RUN button.
Press the GO button.
Everyone: Exit to the calculator Main Menu.
Choose the RESTART option from the calculator Main Menu.
Choose the PICK POINTS option and continue.

Teacher: To start the simulation over with a new group, stop the model by pressing the NetLogo GO button, if it is on.
Have everyone, including yourself, logout of their calculators.
Press the ERASE ALL DATA button on the TISCHOOL site.
Press the NetLogo SETUP button.
Follow these instructions from the beginning again.

BUTTONS:
--------
SETUP - clears all turtles and patches.  This should only be pressed when starting out with a new group of users since all data is lost.
RE-RUN - sets up the model to be able to run again with the same users
GO - runs the simulation
SET RULE - displays an input dialog that allows the leader to enter the verbal challenge.  The entered challenge is then displayed in the CURRENT CHALLENGE monitor.  This is meant for a convenience of the users and has no effect on the actual running of the simulation.
NEXT >>> - shows the next quick start instruction
<<< PREVIOUS - shows the previous quick start instruction
RESET INSTRUCTIONS - shows the first quick start instruction

MONITORS:
---------
MOUSE X - shows the pxcor of the patch the mouse is currently on, or if the mouse is no longer over the graphics window, it displays the pxcor of the patch the mouse was last on
MOUSE Y - shows the pycor of the patch the mouse is currently on, or if the mouse is no longer over the graphics window, it displays the pycor of the patch the mouse was last on
NUMBER OF POINTS AT MOUSE - shows the number of turtles on the patch the mouse is currently on, or if the mouse is no longer over the graphics window, it displays the number of turtles on the patch the mouse was last on
EQUATION - shows the equation for the line of regression if LINEAR-REGRESSION? is true
R^2 - shows the correlation coefficient for the line of regression if LINEAR-REGRESSION? is true
CURRENT CHALLENGE- displays the last challenge that was entered when the SET CHALLENGE button was pressed.  This is meant for a convenience of the users and has no effect on the actual running of the simulation.

SWITCHES:
---------
LINEAR-REGRESSION? - if true, the line of regression is shown.  Otherwise, it is not.


CALCULATOR INFORMATION
----------------------

TEACHER CALCULATOR:
-------------------
Students and teacher have identical calculator programs.

STUDENT CALCULATORS:
--------------------
To enter the simulation, choose the PICK POINTS option.  Move your point around by pressing the ARROW keys.

The DONE softkey returns you to the Main Menu.
The STEP softkey prompts you to change the amount of distance you move when you press an ARROW key.  You can choose from 0.5, 1, and 5.


THINGS TO NOTICE
----------------
What is the least number of points to create an R^2 value 0.0?  1.0?

Why does it not make sense to have a regression line for only 1 data point?

Is it harder to get an R^2 value of a particular value when there are more or less points?  Why?

What happens to the regression line and the correlation coefficient if there are multiple points on a single patch?


THINGS TO TRY
-------------
Challenge the students to make data sets that have correlation coefficients of different values.

Move all the points the same amount in a single direction.  Does the correlation coefficient change?  The equation of the line of regression?  Why?

Find out which points have more effect on the R^2 value and the line of regression.  What qualities do these points have that other points lack?

Set LINEAR-REGRESSION? to OFF.  Challenge the students to make a data set with a certain R^2 value or a particular equation for the regression line.  Turn LINEAR-REGRESSION? ON.  How accurate were they?  What strategies did they use?  Can they be improved?


EXTENDING THE MODEL
-------------------
Support having multiple data sets.  Perhaps each calculator could control a particular data set.

Research other types of regression and support them.


CREDITS AND REFERENCES
----------------------
This activity and associated models and materials was created as part of the project:
PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS.
The project gratefully acknowledges the support of the National Science Foundation ( REPP program ) -- grant number REC #9814682.

Copyright 2000 by Uri Wilensky & Walter Stroup. Updated 2001,2002. All rights reserved.

Permission to use, copy, or modify this software and its associated documentation, models and curricular materials for educational and research purposes only and without fee is hereby granted, provided that this copyright notice and the original authors' names appear on all copies and supporting documentation. For any other uses of this software, in original or modified form, including, but not limited to distribution in whole or in part, specific prior permission must be obtained from Uri Wilensky and Walter Stroup. These programs shall not be used, rewritten, or adapted as the basis of a commercial or hardware product without first obtaining appropriate licenses from Uri Wilensky & Walter Stroup. We make no representations about the suitability of this software for any purpose. It is provided "as is" without express or implied warranty.

To refer to this model in academic publications, please use: Wilensky, U. & Stroup, W. (2000).  NetLogo HubNet Regression model. http://ccl.northwestern.edu/netlogo/models/HubNetRegression. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 2000 by Uri Wilensky and Walter Stroup.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/HubNetRegression for terms of use.
@#$#@#$#@
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car
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Circle -1 false true 183 186 61
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square
true
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thin wedge
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wide wedge
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@#$#@#$#@
NetLogo 2.0beta5
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