Statistics Programs, Curve Fitting | HP 35s Scientific specification

16

Statistics Programs

Curve Fitting

This program can be used to fit one of four models of equations to your data. These models are the straight line, the logarithmic curve, the exponential curve and the power curve. The program accepts two or more (x, y) data pairs and then calculates the correlation coefficient, r, and the two regression coefficients, m and b. The

program includes a routine to calculate the estimates xˆ and yˆ. (For definitions of these values, see "Linear Regression" in chapter 12.)

Samples of the curves and the relevant equations are shown below. The internal regression functions of the HP 35s are used to compute the regression coefficients.

Statistics Programs 16-1

Image 247

HP 35s Scientific manual Statistics Programs, Curve Fitting

Contents

Users guide HP 35s scientific calculator Printing History Contents RPN The Automatic Memory Stack Viewing a Variable ContentsStoring Data into Variables Hyperbolic Functions Real-Number FunctionsQuotient and Remainder of Division Trigonometry Entering π Entering and Evaluating Equations Fractions Vector Arithmetic 10-1 Solving EquationsIntegrating Equations Operations with Complex Numbers Creating Vectors from Variables or Registers 10-8 Base Conversions and Arithmetic and Logic 11-1Statistical Operations 12-1 10-7 Simple Programming 13-1 Part 2. Programming Programming Techniques 14-1 Statistics Programs 16-1 Support, Batteries, and ServicePart 3. Appendixes and Reference Solving and Integrating Programs 15-1 ALG Summary User Memory and the StackMore about Solving How the Integral Is Evaluated Round-Off ErrorMore about Integration Messages Operation Index Contents Part Page Turning the Calculator On and Off Adjusting Display ContrastGetting Started Important Preliminaries Shifted Keys Highlights of the Keyboard and Display2Getting Started Left-shifted function Right-shifted Letter for alphabetic Alpha KeysCursor Keys Function Key 4Getting Started  Clear or CancelBackspacing and Clearing Keys for Clearing Clear menu       Key Description 6Getting Started Using Menusˆ ˆ    HP 35s Menus Chapter Name Other functions Programming Instructions 8 Exiting Menusor   KeysDisplay RPN and ALG Modes Keys Display 10Getting Started RPN mode ALG mode Undo key 12Getting Started Display and AnnunciatorsFirst Line Second Line Annunciators EQN HP 35s Annunciators Meaning Chapter 14Getting Started Making Numbers Negative Keying in NumbersExponents of Ten z 16Getting Started  Understanding Entry CursorRange of Numbers and Overflow  Single Argument or Unary Operations Performing Arithmetic Calculations18Getting Started  Two Argument or Binary OperationsKey RPN,RPN Program ALG, Equation, ALG Program Õ   Key RPN, RPN Program ALG, Equation, ALG Program Controlling the Display Format 22Getting Started Periods and Commas in Numbers   24Getting Started Complex number display format  ,  , 8 8  SHOWing Full 12-Digit Precision8   8× Entering Fractions Fractions26Getting Started  Messages  É Checking Available Memory Calculator Memory28Getting Started Clearing All of Memory 30Getting Started What the Stack Is RPN The Automatic Memory StackRPN The Automatic Memory Stack 2RPN The Automatic Memory Stack Clearing the X-Register X and Y-Registers are in the DisplayReviewing the Stack Press  Exchanging the X- and Y-Registers in the Stack4RPN The Automatic Memory Stack Arithmetic How the Stack Does It 6RPN The Automatic Memory Stack How Enter Works Filling the stack with a constant How to Clear the Stack 8RPN The Automatic Memory Stack Last X Register Correcting Mistakes with Last  Reusing Numbers with Last Ù     Chain Calculations in RPN ModeWork from the Parentheses Out       ExercisesOrder of Calculation        More Exercises     18RPN The Automatic Memory Stack Keys DisplayDescription AStoring Data into Variables Press letter-key  Storing and Recalling Numbers2Storing Data into Variables Press letter-key  G  A  4Storing Data into Variables Using the MEM CatalogViewing a Variable VAR catalog D E C Storage arithmetic uses , , , or  Arithmetic with Stored VariablesStorage Arithmetic 6Storing Data into Variables Recall Arithmetic E Exchanging x with Any Variable D D  Variables I and JA 10Storing Data into Variables Real-Number Functions Exponential and Logarithmic Functions   Power FunctionsQuotient and Remainder of Division   Entering π Trigonometry 4Real-Number Functions Setting the Angular ModeTrigonometric Functions Option Description Annunciator   Percentage Functions Hyperbolic Functions     Const Menu Items Description Value Physics Constants8Real-Number Functions Items Description Value Rectangular/Polar Conversions Conversion Functions10Real-Number Functions 30o 6 812Real-Number Functions Angle Conversions Time Conversions Unit Conversions Probability Probability FunctionsFactorial Gamma  16Real-Number Functions Absolute value Parts of NumbersInteger part Fractional part PressDisplay To calculate18Real-Number Functions Entering Fractions Fractions  Display Rules Fractions in the Display2Fractions Entered Value Internal Value Displayed Fraction Accuracy Indicators Changing the Fraction Display Setting the Maximum Denominator4Fractions  6Fractions Choosing a Fraction Format To Get This Fraction Format Change These Flags   j Examples of Fraction Displays Rounding Fractions Fractions in Equations 10Fractions Fractions in Programs = .25 π d2 l Entering and Evaluating EquationsHow You Can Use Equations Entering and Evaluating Equations 2Entering and Evaluating Equations    D Value   Key Operation Summary of Equation Operations Variables in Equations Entering Equations into the Equation List4Entering and Evaluating Equations Functions in Equations Numbers in Equations  Displaying and Selecting EquationsParentheses in Equations   Ö  8Entering and Evaluating Equations Editing and Clearing Equations Types of Equations 10Entering and Evaluating Equations Evaluating Equations Type of Equation Result for  Result for  Using Enter for Evaluation       Using XEQ for Evaluation12Entering and Evaluating Equations  Responding to Equation Prompts Operator Precedence Syntax of Equations14Entering and Evaluating Equations Equations Meaning Order Operation Example 16Entering and Evaluating Equations Equation FunctionsΣxy Perimeter = a + b + h sin1θ + sin1φ RPN Operation Equation function Area = 18Entering and Evaluating Equations Verifying Equations Syntax Errors Õ 20Entering and Evaluating Equations Markup ⋅ Cost = Price Solving EquationsSolving an Equation Solving Equations = v0 t + 1/2 g t 2Solving Equations   G      P    P  6Solving Equations Solving built-in Equation  Verifying the Result Understanding and Controlling Solve Choosing Initial Guesses for Solve Interrupting a Solve Calculation8Solving Equations Solving Equations Equation 10Solving Equations= 40 H ⋅ 20 H ⋅ 4 ⋅ H Type in the equation H   4H  value 12Solving Equations For More Information Integrating Equations Integrating Equations 2Integrating Equations Integrating Equations FN   J0 x = π 0 cosx sin t dt = t 4Integrating Equations X  SinxX 6Integrating Equations Accuracy of IntegrationSpecifying Accuracy Interpreting Accuracy 8        8Integrating Equations 8 Form  Operations with Complex Numbers Complex Operations Complex Stack2Operations with Complex Numbers Functions for One Complex Number, z To Calculate Press 4Operations with Complex Numbers 8  68  6 6 6 Display Description Using Complex Numbers in Polar Notation 6Operations with Complex Numbers ?  ?  ?  6 ? ? Complex Numbers in Equations        Program lines ALG modeComplex Number in Program    Vector operations Vector ArithmeticVector Arithmetic     Õ 3  3  Absolute value of the vector 10-4Vector Arithmetic Dot product   3 3 3   Angle between vectors Õ   3   Vectors in Equations10-6Vector Arithmetic Program lines Description Vectors in Programs Then hC Õ hA Creating Vectors from Variables or Registers10-8Vector Arithmetic Base Conversions and Arithmetic and Logic Base Conversions and Arithmetic and LogicBase Menu Menu label Description    11-2Base Conversions and Arithmetic and Logic Õ  Logic Menu Arithmetic in Bases 2, 8,11-4Base Conversions and Arithmetic and Logic           Representation of NumbersNegative Numbers   Range of Numbers    Using base in program and equationsWindows for Long Binary Numbers  Entering Statistical Data Statistical OperationsStatistical Operations 12-2Statistical Operations Correcting Errors in Data EntryEntering One-Variable Data Entering Two-Variable Data Initial x, y Corrected x, y   Menu Key Description Statistical CalculationsMean Statistics Menus         Sample Standard Deviation  Linear Regression Population Standard Deviation Linear Regression Menu  ˆ Õ ˆ12-8Statistical Operations         Limitations on Precision of Data12-10Statistical Operations Summation Statistics Summation Values and the Statistics Registers 12-12Statistical Operations Access to the Statistics Registers Statistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming 13-2Simple Programming Area = πx2  X  Selecting a ModeKeysDisplay In ALG mode Designing a Program  letter-key Using RPN, ALG and Equations in ProgramsProgram Boundaries LBL and RTN 13-4Simple Programming Strengths of RPN Operations Data Input and Output 13-6Simple Programming Entering a Program Clear functions and backspace key A Function Names in Programs13-8Simple Programming  R  RPN modeE R 13-10Simple Programming Running a ProgramExecuting a Program XEQ  Keys Display Description RPN mode Testing a Program 13-12Simple Programming Entering and Displaying Data RPN mode ALG mode Using Input for Entering Data 13-14Simple Programming Using View for Displaying Data   ÇR ÇH Using Equations to Display Messages13-16Simple Programming  V  S     Keys RPN mode R H V  R R H   V OL  A RE A   C  value Displaying Information without Stopping  13-18Simple Programming Interrupting a Running Program Error StopsStopping or Interrupting a Program Programming a Stop or Pause STOP, PSE 13-20Simple Programming Editing a Program Viewing Program Memory Program Memory Catalog of Programs MEM Memory Usage13-22Simple Programming Checksum Clearing One or More Programs   Nonprogrammable FunctionsProgramming with Base  Decimal mode set Selecting a Base Mode in a ProgramNumbers Entered in Program Lines 13-26Simple Programming Polynomial Expressions and Horners MethodAx4 + Bx3 + Cx2 + Dx + E A    A X     13-28Simple Programming Programming Techniques Programming TechniquesRoutines in Programs Calling Subroutines XEQ, RTN 14-2Programming Techniques Nested Subroutines A2 + b2 + c2 + d2 14-4Programming Techniques Branching GTOA2 + B2 Programmed GTO Instruction Using GTO from the Keyboard 14-6Programming Techniques Conditional Instructions Test Menus Tests of Comparison x?y, x?0 14-8Programming Techniques Program Lines Description RPN mode Meanings of Flags Flags Clear Flag Fraction-Control Flags14-10Programming Techniques Programming Techniques 14-12Programming Techniques Flags Menu … takes the natural log of the X-input 14-14Programming Techniques  S  value   value Number F      Loops14-16Programming Techniques Conditional Loops GTO 14-18Programming Techniques Loops with Counters DSE, ISG Programming Techniques Variables I and J Indirectly Addressing Variables and Labels14-20Programming Techniques Indirect Address, I and J 14-22Programming Techniques If I/J contains Then I/J will address Equations with I/J Program Control with I/JUnnamed indirect variables 14-24Programming Techniques Solving a Program Solving and Integrating ProgramsSolving and Integrating Programs V= N x R x T 15-2Solving and Integrating Programs P  value   value Keys Display Description ALG modeProgram Lines Description ALG mode G    H P   L  15-6Solving and Integrating Programs Using Solve in a Program label  variable Integrating a Program Program Lines In RPN mode 15-8Solving and Integrating Programs Sin  S   X 15-10Solving and Integrating Programs Using Integration in a Program label   variable Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Curve Fitting Statistics ProgramsStatistics Programs 16-2Statistics Programs = B + MIn Program Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs   S           Logarithmic Exponential PowerNormal and Inverse-Normal Distributions  16-12Statistics Programs Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dx This routine initializes the normal distribution program 16-14Statistics Programs Program Lines Program Lines Program S 16-16Statistics Programs To the inverse D  16-18Statistics Programs Grouped Standard Deviation∑ x f   16-20Statistics Programs Statistics register Index variable used to indirectly address the correctRegister Summation Σ f Summation Σ x i f  U       16-24Statistics Programs TVM equation is Miscellaneous Programs and EquationsTime Value of Money Miscellaneous Programs and Equations NÕ P4 I I P  value KeysDisplay In RPN mode    17-4Miscellaneous Programs and Equations    17-6Miscellaneous Programs and Equations I    Prime Number Generator 17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried 17-10Miscellaneous Programs and Equations   Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Answers to Common Questions Support, Batteries, and ServiceSupport, Batteries, and Service A-1 Calculator Support Environmental Limits 2Support, Batteries, and Service Changing the Batteries Support, Batteries, and Service A-3 4Support, Batteries, and Service Testing Calculator Operation Self-Test Support, Batteries, and Service A-5 6Support, Batteries, and Service Support, Batteries, and Service A-7 Warranty Customer Support 8Support, Batteries, and Service Emea Support, Batteries, and Service A-9 10Support, Batteries, and Service Invent Support, Batteries, and Service A-11 12Support, Batteries, and Service Yyyy+ Support, Batteries, and Service A-13 14Support, Batteries, and Service Managing Calculator Memory User Memory and the StackUser Memory and the Stack B-1 2User Memory and the Stack Resetting the Calculator User Memory and the Stack B-3 Clearing Memory 4User Memory and the Stack DefaultStatus of Stack Lift Category Neutral Operations Disabling OperationsUser Memory and the Stack B-5 ˆ ˆ Status of the Last X Register6User Memory and the Stack Accessing Stack Register Contents 8User Memory and the Stack ALG Summary C-1 ALG SummaryAbout ALG , Simple Arithmetic Doing Two argument Arithmetic in ALG Percentage Calculations Power Functions xÕ Parentheses CalculationsPermutations and Combinations Quotient and Remainder Of Division  4 Õ  Hyperbolic functions Trigonometric Functions ALG Summary C-7 Reviewing the Stack Operations with Complex Numbers Integrating an Equation8ALG Summary ALG Summary C-9 6 6Õ4 6 8Ë4 66  Entering Statistical Two-Variable Data Z6 z Σ12ALG Summary ALG Summary C-13   ˆ Õ ˆ 14ALG Summary How Solve Finds a Root More about SolvingMore about Solving D-1 Function Whose Roots Can Be Found 2More about Solving More about Solving D-3 Interpreting Results 4More about Solving X  X X  X  XX X  XÕ  6More about Solving More about Solving D-7 X  X4 X Õ   X   When Solve Cannot Find a Root8More about Solving    XMore about Solving D-9 10More about Solving X    X  More about Solving D-11 X4 X ÕÕ 12More about Solving X    X   Round-Off ErrorMore about Solving D-13 14More about Solving How the Integral Is Evaluated More about IntegrationMore about Integration 2More about Integration Conditions That Could Cause Incorrect Results ∞ xe−xdx 4More about Integration   More about Integration 6More about Integration   Conditions That Prolong Calculation Time 8More about Integration More about Integration 10More about Integration Messages F-1 Messages Or program. This might take a while 2Messages Messages F-3    Solve include EQN and PGM modecannot find 4Messages Messages F-5 FN each uses a level, they can also generate this error 6Messages Name Keys and Description Operation IndexOperation Index G-1 Ø ×2Operation Index Operation Index G-3 4Operation Index =  Denominator Operation Index G-5 6Operation Index  Fractional part Operation Index G-7Natural exponential label  8Operation Index  Integer part ISG variable variable Operation Index G-9 Input variable variable Natural logarithm 10Operation Index LBL label label Degrees to radians. Returns 2π/360 Operation Index G-11RCL variable  Pause 12Operation Index Operation Index G-13 XEQ label label 14Operation IndexHyperbolic Tangent View variable variable Operation Index G-15 ÕÕ≠ Õ≤ 11-4 16Operation Index=y? 14-7 Menu ≠0? Operation Index G-17 Power 18Operation Index Index-1 Index Index-2 EQN List TOP 6-7, F-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Angle between two vectors Index-11 Index-12