STATISTICS: Pearson r

Introduction: Pearson r - the mean of the z-score products for X and Y pairs, where X stands for one variable and Y stands for the other. The range of the Pearson r is from +1 to -1. A positive value for r indicates a direct relationship between the variables, a negative value indicates an inverse relationship. Anything close to r = 0 indicates no relationship between the variables.
 
 Pearson r Formula  formula%20Pearson%20r  
  Note: This program is in TI-BASIC and can be entered into the calculator by the calculator keyboard. Do not enter the outline, line numbers or comments, they are for reference only. The example programs below are for testing the program. If you get the values listed, the program was entered correctly. If not, check the listing and correct it. The program has been checked and tested.
  Note: -> is the [STO->] on the calculator keyboard.
  Note: click on the underline text in Outline to go to that line number
    Program Memory = 760
 
Pearson r Outline:
Line 1. Clear Screen
Line 2 - 8. Instructions
Line 12 - 18. Lbl D: Data Input
Line 22 - 23. Input List 1
Line 24 - 25. Input List 3
Line 27 - 32. Calculator formula
Line 34 - 39. Disp List 1
Line 40 - 43. Disp List 3
Line 47 - 52. Pearson r Formula
Line 61 - 64. formula
Line 69 - 72. Formula calculations
Line 74 - 81. Output    r =
Line 79 - 83. Input   regression prediction terms
Line 86 - 87. calculations    Y predicted from X
Line 90 - 93. Output
  Pearson r Examples
  Reference
  Reference Links
 

PEARSON r

Line Command or Statement Comments
   1. ClrHome  Clear Screen
   2. Disp "SELECT LIST OR" Instructions
   3. ,"DATA TO BEGIN -"       |
   4. ,"SELECT ''STAT LIST''        |
   5. ,"OR LIST"       |
   6. Pause 
   7. ,"USE COMMAS BTWN"       |
   8. ,"NUMBERS IN LIST"       |
   9.  ,"ENTER n, Σx, Σx²"        |
 10.  ,"Σy, Σy², Σxy"        |
 11. ,"FOR DATA"  End Instructions
 12. Pause 
 13. ClrHome
 14. Menu("PEARSON r","LIST",L,"STAT LIST",S,"DATA",D 
 15. Lbl D Data input
 16. Input "n =",N n
 17.  Input "Σx =",X  Σx
 18.  Input "Σx² =",U  Σx²
 19.  Input "Σy =",Y  Σy
 19.  Input "Σy² =",V  Σy²
 20.  Input "Σxy =",W  Σxy
 21. Goto F formula
 22. Lbl S Stat List input
 23. Disp "STAT LIST 
 24. Input "L1",L1 STAT L1
 25. Input "L2:",L2 STAT L2
 26. Goto T calculations from List
 27. Lbl L List input
 28. Disp "DATA LIST 
 29. Input "L1=",Str1 L1
 30. expr("{"+Str1->L1 
 31. Input "L3=",Str3 L3
 32. expr("{"+Str3->L3 
 33. ClrHome 
 34. Lbl T calculations from List
 35. dim(L1->N  n
 36.  sum(L1->X  Σx
 37.  sum(L1²->U  Σx²
 38.  sum(L3->Y  Σy
 39.  sum(L3²->V  Σy²
 40.  sum(L1L3->W  Σxy
 41. Float 
 42. Disp "n = 
 43. Output (1,4,N n =
 44.  Disp "Σx =  
 45.  Output (2,5,X  Σx =
 46.  Disp "Σx² =  
 47.  Output (3,6,U  Σx² =
 48.  Disp "Σy =  
 49.  Output (4,5,Y  Σy =
 50.  Disp "Σy² =  
 51.  Output (5,6,V  Σy² =
 52.  Disp "Σxy =  
 53.  Output (6,5,W  Σxy =
 54.  Pause 
 55.  Lbl F Pearson r  formula
 48.  Float 
 49.  (N)(W)-(x)(y)->A  NΣxy-ΣxΣy->A
 50.  ((N)(U)-((x)²))->B  NΣx²-(Σx)²->B
 51.  ((N)(V)-((y)²))->C  NΣy²-(Σy)²->C
 52.  A/√(BC)->D  A/√(BC)->D
 53. Fix 4 
 54. Output(8,1,"r = output Pearson r
 54. Output(8,4,D Answer Pearson r
 55. Pause 
 56. ClrHome 
 57. Float 
 58. X/N->Q x
 59. Y/N->R y
 60. Float 
 61. (U-((x)≤)/N)->K prediction (formula) calculations
 62.  √(K/(N-1))->O  
 63. (V-((y)≤)/N)->L 
 64.  √(L/(N-1)->P  
 65. Fix 4 prediction (formula) input from List
 66. Disp "x = x =
 67. Output(1,4,Q 
 68. Disp "Sx = Sx =
 69. Output(2,5,O 
 70. Disp "y = y =
 71. Output(3,4,R 
 72. Disp "Sy = Sy =
 73. Output(4,5,P 
 74. Pause 
 75. X/N->Q  x
 76. Y/N->R y
 77. Goto O 
 78. Lbl P prediction (formula) input
 79. Input"x =",Q x =
 80. Input "y =",R y =
 81. Input "Sx =",O Sx =
 82. Input "Sy =",P Sy =
 83. Input "r =",D r =
 84. Lbl O 
 85. Float 
 86. (DP)/O->G  prediction calculations (formula)
 87. (R-(((D)(P))/O)Q)->H 
 88.  Fix 3  
 89.  Disp ""  
 90.  Disp "Y =  Y =
 91.  Output(6,3,G  
 92.  Output(6,8, "X  
 93.  Output(6,10,H  Answer Prediction
 94.  Pause  
 95.  ClrHome  
 
Pearson r Example 1:
List 1: 77, 74, 73, 72, 70, 70, 69, 68, 67, 67, 66, 64, 63, 60
List 2: 47.1, 45.5, 46.2, 46.1, 42.8, 38.3, 45.4, 36.5, 42.1, 37.2, 34.1, 35.1, 33.1, 33.0
Data: n = 14,  Σx = 960,  Σx² = 66,102   Σy = 562.5  Σy² = 22,976.13  Σxy = 38,852.5
Answers: n = 14,  Σx = 960,  Σx² = 66,102   Σy = 562.5  Σy² = 22,976.13  Σxy = 38,852.5  r = .88  Y = 1.03X - 30.45
 
Pearson r Example 2:
List 1: 100, 40, 95, 90, 92, 85, 55, 60, 98, 20
List 2: 0, 95, 5, 20, 30, 40, 50, 70, 0, 100
Data: n = 10,  Σx = 735,  Σx² = 61,043   Σy = 410  Σy² = 29,350  Σxy = 21,185
Answers: n = 10,  Σx = 735,  Σx² = 61,043   Σy = 410  Σy² = 29,350  Σxy = 21,185  r = -.95  Y = .89X + .38
 
Reference:
TI Basic Commands or Statements:
  augment( listA, listB)   Returns a list, which is list B appended to the end of list A
  ClrHome  clears home screen
  dim(  returns the dimension (number of elements) of list
  Disp  displays text or value specified
  End  identifies end of For(, If-Then-Else, Repeat, or While loop
  expr(  converts string to an expression
  Fix  sets fixed-decimal mode for number of decimal places
  Float  sets floating decimal mode. Displays decimal with no trailing zeros
  For( variable,begin,end[increment])    Executes commands through End, incrementing variable from begin by increment until End.
  Goto  goes to label specified. Goto requires a line label be implemented as a destination
  If; Then; Else  Executes commands from Then to Else If condition true: or from Else to End if condition false
  Input  prompts for value to store to variable. Requires user input through keypad.
  Lbl  creates a label of one or two characters
  Menu  generates a menu of up to seven items
  min( valueA, valueB)  Returns smaller of value A and Value B
  output( row, column)  displays text or value beginning at specified row and column
  round( value [,# decimals])   returns a number rounded to # decimals (=<9)
  seq( expression, variable, begin, end[, increment])   Returns list created by evaluating expression with regard to variable, from begin to end by increment
  SortA( listname)   Sorts elements of listname in ascending (count up) order
  Str# (# is number)   String: A sequence of characters is called a string
  sum(  returns the sum of elements in list
  While condition  Executes commands while condition is true until end
 
Statistics Reference:
Information or Links:
Statistical Inference on the TI-83
This site contains typical problems and solutions on the general statistics topics of probability distributions, confidence intervals, hypothesis testing, analysis of variance, and correlation analysis.
http://www.wku.edu/~david.neal/statistics/
Using the TI-83 graphing calculator tutorial
  General Info - Algebra 1 - Statistics 1 - Algebra 2 - Trigonometry - Statistics 2 - PreCalculus - Calculus
http://mathbits.com/mathbits/TISection/Openpage.htm
TI-83 Video Tutorials
This series of tutorials for the TI-83 (or TI-83 Plus)Currently, only the chapters on single population confidence intervals, population hypothesis test, linear regression, Chi-Square and ANOVA are completed.
http://student.ccbcmd.edu/elmo/math141s/TIVideo/TIWebpage.htm
United TI Forums - TI Basic
  TI-Basic - Use this forum to post questions and discuss the TI-BASIC programming language.
http://www.unitedti.org/index.php?showforum=4
Hints for Statistics Using a TI-83
http://www.math.wustl.edu/~sawyer/handouts/StatTI83.html#sampmean
  If you want the TI-83 to calculate the Pearson correlation coefficient r (which is the same as the Model R2 = r2 for the linear regression), you must turn "Diagnostics'' ON by entering 2nd 0 (for CATALOG), space down to DiagnosticOn, press ENTER, and then ENTER again if you see DiagnosticOn on a different screen
Quick-and-Dirty Guide to the TI-83, TI-83+, TI-84, and TI-84+
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/ti.html
  The TI-83 "Plus", TI-84, and TI-84 "Plus" are almost identical, so this guide will serve just as well for them.
Getting y^ from Any x in a Regression on the TI-83/84/89
http://www.tc3.edu/instruct/sbrown/ti83/yhat.htm
  The regression line represents the model that best fits the data. This page shows you three methods, which all yield the same answer
Intro to Programming TI-83/83+ BASIC
http://odin.prohosting.com/mjs2k/tutorials/index.htm
  Here you will find several tutorials to help you learn how to write programs on your TI-83, TI-83+ calculator(s). NO PROGRAMMING EXPERIENCE IS NECESSARY
Statistical Inference on the TI-83+
http://www.wku.edu/~david.neal/statistics/
  This site contains typical problems and solutions on the general statistics topics of probability distributions, confidence intervals, hypothesis testing, analysis of variance, and correlation analysis. Detailed survey sampling projects are also included.
http://www.hsu.edu/default.aspx?id=3617
  TI-83/84 programs
http://101science.com/Ticalcpgms.htm
  Links to TI-83 Programs you can download to your calculator
http://www.angelfire.com/pro/fkizer/Instructions/tishrtusrguide83.htm
  Brief Users Guide for the TI-83 Plus
Interactive TI-83 Plus Tutorial
  TI-83 Plus Tutorial by Mathematics Department, SCSU.
TI-83/84/89/92 Procedures and Help
  This page points you to step-by-step procedures for several tasks on the TI-83
Business Statistics
  Calculating Statistics Using the TI-83 or Using Excel
DevHardware TI-83/84 forums
  Programming forum discussing coding and everything related to the well-known TI-83/84 graphing calculators
Math 320 (Statistics) Excel and Calculator Notes
  specific procedures for Excel or a TI-83
Pearson's r calculator
  Online calculator for Pearson r
 
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