Two-variable, Columns for a linear fit only

Two-variable

Statistic	Definition

MEANX	Mean of x- (independent) values.
ΣX	Sum of x-values.
ΣX2	Sum of x2-values.
MEANY	Mean of y- (dependent) values.
ΣY	Sum of y-values.
ΣY2	Sum of y2-values.
ΣXY	Sum of each xy.
SCOV	Sample covariance of independent
	and dependent data columns.
PCOV	Population covariance of independent
	and dependent data columns
CORR	Correlation coefficient of the
	independent and dependent data
	columns for a linear fit only
	(regardless of the Fit chosen). Returns
	a value from 0 to 1, where 1 is the best
	fit.
RELERR	The relative error (for the selected fit).
	Provides a measure of accuracy for
	the fit.

8-14	Statistics aplet

Page 106

Image 106

HP 40G manual Two-variable, Columns for a linear fit only

Contents

USER’S Guide Page Contents Parametric aplet Inference aplet Importing Sample Statistics from the Statistics aplet Variables and memory management Programming Index @, &26@, +20@, etc PrefaceManual conventions +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc Preface Getting started On/off, cancel operationsHome Display To adjust the contrast To clear the displayParts of the display Menu keys KeyboardAnnunciator Description Aplet control keys Key Meaning 175@ +,7@$/3+$@ 75@ Key Description Shifted keystrokesHelpwith +,7@$/3+$@ Program commands Inactive keys Math keys Menus To cancel a menuTo search a menu Setting Options Mode settingsReset input form values Input forms Setting Options Aplets E-lessons Setting a modePress+20@ to return to Home Aplet Use this aplet to explore Name Quad Explorer aplet N T Trig Explorer aplet *,*A, keys Aplet views Symbolic view Plot view Numeric viewAplet library Aplets are stored in the Aplet library Views menu contains the Plot-Table view Configuration Aplet view configurationPlot Setup Numeric Setup Symbolic To change views Long results Negative numbers Mathematical calculationsEntering expressions Example Explicit and implicit multiplication Scientific notation powers@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ +,7@√ 85@9 Entering Calculates@ 45 @6+,7@π +,7@√ @85 @9 @ Clearing numbers Using previous results 175@ updates ANS from 50 to 75 to 50175@ @25 175@175@ $/3+$@ a 175@ Accessing the display historyKey Function See Setting fraction precision below for more information Using fractionsSetting Fraction mode Clearing the display history Setting fraction precision @@@2@3 Fraction calculations Converting decimals to fractionsReturn to Home and enter the calculation Evaluate the calculation Complex results To enter complex numbers Complex numbersConverting a number to a fraction + iy Catalogs and editors Catalog/Editor ContentsStoring complex numbers Statistics Pred function Differences between the HP 38G and the HP 39G/40GMemory manager Plot Goto function Trig Explorer and Quadratic Explorer apletsPage Aplets and their views About the Symbolic viewDefining an expression Symbolic view Aplet views Aplets and their views Aplets Evaluating expressionsHome $7+@ Symb view keys$56@ +,7@CLEAR About the Plot view Setting up the plot Plot view setupPlot view settings 175@ or Reset plot settings Plot view keys Exploring the graph+,7@*A To jump directly to a value To turn trace on/ off Trace a graphZoom within a graph Zoom options Divides vertical scale only, using Divides horizontal scale only, usingMultiplies horizontal scale, using Multiplies vertical scale only, using Press *k, to move to the bottom of the Zoom list 018Zoom=220Un-zoom =220Zoom Out =220Y-Zoom =220X-Zoom=220X-Zoom Out =220Y-Zoom Out To box zoom To set zoom factors Other views for scaling and splitting the graph Options Menu key copies the right plot to the left Decimal scaling About the numeric viewOverlay plots Integer scaling Trigonometric scaling Numeric view settings Setting up the table numeric view setupReset numeric settings NUM view menu keys Exploring the table of numbersZoom within a table Column, then enter the value to jump to Building your own table of numbersArrow keys to place the cursor in the independent variable 175@, the values for the dependent variables are Build Your Own menu keys Clear data $3/7@ Select Example plotting a circle+,7@√@9 Getting started with the Function aplet Function apletAbout the Function aplet Open the Function aplet @75@175@ Define the expressionsPlot the functions Plot the functions Trace the linear function Change the scale Trace a graphWith FCN functions Times SelectRoot Find the greater of the two roots of the quadratic functionRoot value is displayed at the bottom of the screen Choose the end value for 2Select.SlopeMove the cursor to x = 1 by pressing the *A,or @.2 To find the extremum of the quadratic Display the numeric view Set up the tableDisplay the numeric setup Display the numeric view Display a table of numeric values Match the table settings to the pixel columns in the graphExplore the table Move to X = Function aplet interactive analysis Area Extremum Isect Root Slope Access FCN variables FCN functions Function Description Cursor. You need to have at least Symbolic view. DisplaysTwo selected expressions =  Plotting a piecewise defined function example$3/ @ Select Page Getting started with the Parametric aplet Parametric apletAbout the Parametric aplet Open the Parametric aplet Define the expressions +,7@PLOT Set angle measure Set up the plot Plot the expression360 +,7@ Plot Overlay plot Display the numbersPlot a triangle graph over the existing circle graph 120Page Open the Polar aplet Polar apletGetting started with the polar aplet +,7@CLEAR 46+,7@π 2.a Explore the graph Display the numbers About the Sequence aplet Sequence aplet starts in the Symbolic viewSequence aplet Getting started with the Sequence aplet Define the expression Keys to assist in the entry of equations Plot the Fibonacci sequence Plot Setup, set the Seqplot option to CobwebPlot the sequence Display the table Select CobwebPage Solve aplet About the Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Define known variables Solve for the unknown variable a Solve the unknown variable Plot the equation@ Select Auto Solve aplet’s NUM view keys ≈20 times Use an initial guess Number format Interpreting results Message Condition Root- Finder at work $/3+$@X Plotting to find guessesAt2 x = v0t + 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T Plot the graph To move cursor to the intersection Initial guess Using variables in equationsHome variables 3175@*k,*k,*k Getting started with the Statistics aplet Statistics apletAbout the Statistics aplet 1400 920 1100 2265 2890 2200 To move to the next column Open the Statistics aplet Enter data175@1 175@ 175@5 175@ 175@4 175@ 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Select a fit in the Symbolic setup view Choose fit and data columns Explore statistics Setup plotSelect2. Linear Display the equation for the best linear fit To move to the FIT1 +2field To highlight Entering and editing statistical data$7+@ S to highlight 6175@ Statistics aplet’s NUM view keys +,7@ FXUVRU 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Before re-use Sets will need to be selected againHeight cm Frequency Save data Angle SettingDelete data To choose the fit Defining a regression model 2VARInsert data Sort data values Select the Sort Order option. You can choose either = m lnx + b Fit models To define your own fitFit model Meaning = ax3+bx2+cx+d. Needs at least One-variable Computed statisticsStatistic Definition Two-variable Columns for a linear fit only To plot statistical data PlottingYou can plot Plot types Histogram Box and Whisker Plot Scatter Plot Correlation Relative ErrorFitting a curve to0182VAR data Coefficient Setting up the plot Plot setup view Plotting mark 2VAR Connected points 2VAR Trouble-shooting a plot Statistics aplet’s Plot view keys Calculating predicted values Find predicted valuesPage About the Inference aplet Default the input form contains example data. This exampleInference aplet Example data Inference aplet’s Symb view keys Getting started with the Inference apletOpen the Inference aplet Hypothesis Tests Confidence Intervals Define the inferential method ∝.a∝ Field name Definition Plot test results Open Statistics aplet. Note Reset current settingsImporting Sample Statistics from the Statistics aplet Open the Statistics aplet Calculate statistics Open Inference aplet @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Import the data Choose inference method and type2one.a E, to move to Field Display Numeric view Display Plot viewSpecify a 90% confidence interval in the C field Display the confidence interval in the Plot view Menu name Hypothesis testsOne-Sample Z-Test Inputs Results Two-Sample Z-TestResult Description One-Proportion Z-Test Successes in the two populations is equal Two-Proportion Z-TestH0 π1 = π2 Selected hypothesis against the null hypothesis. The null One-Sample T-TestTest 1 ∝ Hypothesis is that the sample mean has some assumed value Two-Sample T-Test Sample 1 standard deviation Sample 2 standard deviation Perform are based on the Normal Z-distribution or Student’s Confidence intervalsConfidence interval calculations that the HP 39G/40G can Confidence level Confidence interval for the difference between the means Two populations, ∝1 ∝2, when the population standardTwo-Sample Z-Interval Deviations, σ1 and σ2, are known One-Proportion Z-Interval Sample success count Sample 1 success count Two-Proportion Z-IntervalSuccesses in two populations Sample 2 success count One-Sample T-Interval Two-Sample T-Interval Page Math functions Using mathematical functionsMath menu Function categories To select a functionCalculus Loop Stat-Two Complex Matrices Syntax Math functions by categoryFunctions common to keyboard and menus Keyboard functions +,7@ATAN +,7@ASIN+,7@ACOS +,7@√ ABSvalue Valuepower+,7@ABS +,7@ n Variableexpression Calculus functionsTaylor Lower,upper,expression,variable ARG Complex number functionsConj Constants Hyperbolic trigonometry EXP List functionsAlog EXPM1 Iterate Loop functionsMatrix functions Recurse Polyeval Polynomial functionsPolycoef Polyform Perm Probability functionsComb Random Utpn UtpcUtpf Utpt Real-number functions INT HMS→→HMS Mant Total MODChange RAD→DEG Truncate Statistics-TwoSign Xpon LINEAR? Symbolic functionsIsolate Quad Quote Trigonometry functions Using formal variables Symbolic calculationsSymbolic calculations in the Function aplet Home GG@$/3+$@S1 Finding derivativesTo find derivatives Evaluate the function To find derivatives in the Function aplet’s Symbolic view GG@@$/3+$@ Show the result format To find the indefinite integral using formal variables+,7@GG@0 @ $/3+$@ S1 @ 3 @ Thus, substituting X for S1, it can be seen that 10-26 Variables and memory management Introduction Numeric Precision Storing and recalling variablesTo store a value To store the results of a calculation Calculations Vars menuTo use variables 65 @$/3+$@A 175@ Names or values of variables into programs +,7@LIST $/3+$@L3175@ 2contents,.a is copied to the command line$56@ *e,*e,*e,*A List names directly from the keyboard Category Available names Aplet variables To access an aplet variableTo copy the value of the variable into the edit line Is displayed Memory ManagerStart the Memory Manager. a list of variable categories +,7@MEMORYPage Matrices MatricesVectors Matrix Variables + 7@CLEAR Creating and storing matricesMatrix Catalog keys +,7@*e, or To create a matrix in the matrix catalog Select the type of matrix to create Clears all elements from the matrix Working with matricesTo transmit a matrix +,7@*k, *e 728 672? 175@ 2175@*e 175@ 4175@ Matrix arithmeticTo multiply and divide by a scalar 175@ 8 175@ $/3+$@M1@ $/3+$@M2 175@ $/3+$@M1 j@$/3+$@M2 175@ 175@7 175@ Solving systems of linear equations+,7@MATRIX1 175@ +,7@MATRIX Matrix functions and commands About functions Argument conventions Idenmat EigenvalEigenvv Inverse Rref RankRownorm Schur TRN ExamplesTrace Identity Matrix Transposing a Matrix Reduced-Row Echelon Form Create a list in the List Catalog ListsCreating lists Open the List catalog List catalog keys Create a list List edit keys To display one element To edit a list Displaying and editing listsTo display a list @ /@ 16a*e To insert an element in a list To store one element To delete a list Deleting listsTransmitting lists To delete all lists List functions $7+@L *A,Select $/3+$@L 5175@ $7+@L *A$/3+$@L5175@ $/3+$@A @ Calculates the number of elements in a list Calculates the product of all elements in listPOSlist, element Sorts elements in ascending order 89@65@ 0@89 Finding statistical values for list elements$/3+$@ L1 175@ 180@67$76a Go to the Numeric view To display calculated statisticsPage +,7@letter Aplet note viewTo write a note in Note view Your work is automatically saved. Press any view key +,7@%.63$= +,7@ Cmds Sketch keys Aplet sketch viewTo draw a line To draw a box Where you want any corner of the box to beYou can adjust the size of the box by moving the cursor Draw keys Press 2.again to affix the label KeysHighlight2. the variable name you want to use and press +,7@NOTEPAD To import a graphics variableTo create a note Name of the note is ‘MYNOTE’ Transmits the selected note to Opens the selected note forBegins a new note, and asks for Another HP 39G/40G or PC 14-8 Contents of a Program Structured Programming Programming Program catalog Open Program catalog Program catalog keys +,7@*k, or *e Creating and editing programs Create a new program A,*e Enter commands Edit a program+,7@CMDS To enter functions more to come Editing keys Debug a program Stop a program Using programsRun a program From HOME, type RUN programname. or Program Working with programsCopy a Transmit a program Delete a program Delete all Delete the contents of a programAbout customizing an aplet Programs Customizing an aplet example Aplet naming convention$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Check Programming commandsAplet commands Select Command syntax Syntax for the command is as follows Auto-run programs IF...THEN...END Branch commandsUncheck If test-clause ELSE... END CASE...END Iferr Then Iferr trap-clause Then error-clause ENDIF... then END Drawing commands Graphic commands Grobor →GROBGrobnot Grobxor Loop commands Matrix commands Scale RandmatRedim Scaleadd Print commands Prompt commands Disp linenumbertextitem DispDisptime Editmat matrixname Getkey Input nametitle,labelhelpdefaultInput Wait MsgboxPrompt Wait seconds Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Area Storing and retrieving variables in programsPlot-view variables Axes FastRes CoordExtremum Grid InvCross HwidthIndep Isect Root Nmin / NmaxRecenter S1mark-S5mark StatPlot SimultSlope Umin/Umax Tstep Tmin / TmaxTracing Xcross Xmin / Xmax XtickYtick Ymin / Ymax Yzoom Symbolic-view variablesXzoom Angle U1...U9, U0 X1, Y1...X9,Y9 X0,Y0R1...R9, R0 E1...E9, E0 C1...C9, C0 Numeric-view variablesDigits NumFont FormatNumCol NumIndep NumStep NumRowNumStart NumType PageNum Extending aplets Creating new aplets based on existing aplets $/3+$@ H 175@ $1@ $/3+$@ θ @ Aplet Keys$/3+$@ C @ 175@ $3/ @Select 180@ 35 175@ Solve for the missing Resetting an apletDownloading e-lessons from the web Length of the ladder is approximately 8.72 metres Sending and receiving aplets To transmit an aplet To sort the aplet list Sorting items in the aplet library menu listTo delete an aplet Regulatory information Reference informationCanada LED safety Warranty Reference information Resetting the HP 39G/40G To reset using the keyboard If the calculator does not turn on To erase all memory and reset defaults21@ key Glossary Cross matrix1,matrix2 Operating details Operating temperature 0 to 45C 32 to 113FBatteries Home variables are Menu maps of the Vars menuCategory Available name Modes Function aplet variablesUser-named Function aplet variables are Plot-FCN Parametric aplet variablesParametric aplet variables are Polar aplet variables Polar aplet variables are Sequence aplet variables Sequence aplet variables are Solve aplet variables Solve aplet variables are Statistics aplet variables are Statistics aplet variablesStat-One Math functions are Menu maps of the Math menuMath functions Calculus Polynom = = Program constants Program commands Category Command Message Meaning Selected status messages+,7@ Memory Or intersection is not visible Function value, root, extremumCurrent screen Index Index Index Index Index Index Index Index Index Index Index Index Index

Two-variable

Statistic

columns for a linear fit only