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Calculation of the Correlation Coefficient r, Coefficient of Determination, and Mean Square Error MSe

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u Calculation of the Correlation Coefficient (r), Coefficient of Determination (r2) and Mean Square Error (MSe) After the regression formula parameters on the regression calculation result screen, the following parameters also appear on the display. The parameters that appear depend on the regression formula. Correlation coefficient (r) Displayed following: linear regression, logarithmic regression, exponential regression, or power regression calculation. Coefficient of determination (r2) Displayed following: linear regression, quadratic regression, cubic regression, quartic regression, logarithmic regression, exponential regression, power regression calculation. Mean square error (MSe) Displayed following any regression calculation except Med-Med. Depending on the regression calculation type, mean square error (MSe) is obtained using the following formulas. Σ • Linear Regression (ax + b MSe = 1 n - 2 n (yi - (axi + b))2 i=1 Σ (a + bx MSe = 1 n - 2 n i=1 (yi - (a + bxi))2 Σ • Quadratic Regression MSe = 1 n - 3 n i=1 (yi - (axi2+ bxi + c))2 Σ • Cubic Regression MSe = 1 n - 4 n (yi - (axi3+ bxi2+ cxi + d ))2 i=1 Σ • Quartic Regression MSe = 1 n - 5 n (yi - (axi4+ bxi3 + cxi2 + dxi + e))2 i=1 Σ • Logarithmic Regression MSe = 1 n - 2 n i=1 (yi - (a + b ln xi ))2 Σ • Exponential Regression (a·ebx) .......MSe = 1 n - 2 n (ln yi - (ln a + bxi ))2 i=1 Σ (a·bx)........MSe = 1 n - 2 n i=1 (ln yi - (ln a + (ln b) · xi ))2 6-24

Section	Page
Contents	3
Getting Acquainted — Read This First!	6
Chapter 1 Basic Operation	8
1. Keys	8
2. Display	10
3. Inputting and Editing Calculations	14
4. Using the Math Input/Output Mode	20
5. Option (OPTN) Menu	34
6. Variable Data (VARS) Menu	35
7. Program (PRGM) Menu	38
8. Using the Setup Screen	39
9. Using Screen Capture	43
10. When you keep having problems...	44
Chapter 2 Manual Calculations	47
1. Basic Calculations	47
2. Special Functions	53
3. Specifying the Angle Unit and Display Format	58
4. Function Calculations	60
5. Numerical Calculations	70
6. Complex Number Calculations	80
7. Binary, Octal, Decimal, and Hexadecimal Calculations with Integers	84
8. Matrix Calculations	87
9. Metric Conversion Calculations	104
Chapter 3 List Function	108
1. Inputting and Editing a List	108
2. Manipulating List Data	114
3. Arithmetic Calculations Using Lists	120
4. Switching between List Files	124
5. Using CSV Files	125
Chapter 4 Equation Calculations	128
1. Simultaneous Linear Equations	128
2. High-order Equations from 2nd to 6th Degree	130
3. Solve Calculations	131
Chapter 5 Graphing	133
1. Sample Graphs	133
2. Controlling What Appears on a Graph Screen	136
3. Drawing a Graph	145
4. Saving and Recalling Graph Screen Contents	152
5. Drawing Two Graphs on the Same Screen	155
6. Manual Graphing	157
7. Using Tables	162
8. Modifying a Graph	168
9. Dynamic Graphing	172
10. Graphing a Recursion Formula	175
11. Graphing a Conic Section	180
12. Drawing Dots, Lines, and Text on the Graph Screen (Sketch)	182
13. Function Analysis	184
Chapter 6 Statistical Graphs and Calculations	194
1. Before Performing Statistical Calculations	194
2. Calculating and Graphing Single-Variable Statistical Data	201
3. Calculating and Graphing Paired-Variable Statistical Data (Curve Fitting)	207
4. Performing Statistical Calculations	215
5. Tests	225
6. Confidence Interval	239
7. Distribution	242
8. Input and Output Terms of Tests, Confidence Interval, and Distribution	258
9. Statistic Formula	261
Chapter 7 Financial Calculation	265
1. Before Performing Financial Calculations	265
2. Simple Interest	267
3. Compound Interest	268
4. Cash Flow (Investment Appraisal)	271
5. Amortization	273
6. Interest Rate Conversion	276
7. Cost, Selling Price, Margin	277
8. Day/Date Calculations	278
9. Depreciation	279
10. Bond Calculations	281
11. Financial Calculations Using Functions	284
Chapter 8 Programming	285
1. Basic Programming Steps	285
2. Program Mode Function Keys	286
3. Editing Program Contents	288
4. File Management	290
5. Command Reference	295
6. Using Calculator Functions in Programs	312
7. Program Mode Command List	335
8. CASIO Scientific Function Calculator Special Commands ⇔ Text Conversion Table	343
9. Program Library	350
Chapter 9 Spreadsheet	352
1. Spreadsheet Basics and the Function Menu	352
2. Basic Spreadsheet Operations	354
3. Using Special Spreadsheet Mode Commands	370
4. Conditional Formatting	372
5. Drawing Statistical Graphs, and Performing Statistical and Regression Calculations	378
6. Spreadsheet Mode Memory	385
Chapter 10 eActivity	388
1. eActivity Overview	388
2. eActivity Function Menus	389
3. eActivity File Operations	391
4. Inputting and Editing Data	393
Chapter 11 Memory Manager	411
1. Using the Memory Manager	411
Chapter 12 System Manager	424
1. Using the System Manager	424
2. System Settings	424
Chapter 13 Data Communication	432
1. Performing Data Communication between the Calculator and a Personal Computer	434
2. Performing Data Communication between Two Calculators	441
3. Connecting the Calculator to a Projector	447
Chapter 14 Geometry	448
1. Geometry Mode Overview	448
2. Drawing and Editing Objects	458
3. Controlling the Appearance of the Geometry Window	480
4. Using Text and Labels in a Screen Image	484
5. Using the Measurement Box	488
6. Working with Animations	503
Chapter 15 Picture Plot	512
1. Picture Plot Function Menus	514
2. Managing Picture Plot Files	516
3. Using the Plot Function	518
4. Using the Plot List	524
5. Common Functions with the Graph Mode	529
Appendix	530
1. Error Message Table	530
2. Input Ranges	543
E-Con2 Application	545
1. E-Con2 Overview	546
2. Using the Setup Wizard	547
3. Using Advanced Setup	553
4. Using a Custom Probe	564
5. Using the MULTIMETER Mode	568
6. Using Setup Memory	569
7. Using Program Converter	572
8. Starting a Sampling Operation	575
9. Using Sample Data Memory	578
10. Using the Graph Analysis Tools to Graph Data	580
11. Graph Analysis Tool Graph Screen Operations	584

Match case Limit results 1 per page

6-24

Calculation of the Correlation Coefficient (r), Coefficient of Determination

) and Mean Square Error (MSe)

After the regression formula parameters on the regression calculation result screen, the

following parameters also appear on the display. The parameters that appear depend on the

regression formula.

Correlation coefficient (r)

Displayed following: linear regression, logarithmic regression, exponential regression, or power

regression calculation.

Coefficient of determination (r

)

Displayed following: linear regression, quadratic regression, cubic regression, quartic

regression, logarithmic regression, exponential regression, power regression calculation.

Mean square error (MSe)

Displayed following any regression calculation except Med-Med.

Depending on the regression calculation type, mean square error (MSe) is obtained using the

following formulas.

• Linear Regression (

)

.............

(

)

.............

• Quadratic Regression

.....................

• Cubic Regression

...........................

• Quartic Regression

........................

• Logarithmic Regression

..................

• Exponential Regression (

)

.......

(

)

........

MSe

– 2

(

– (

))

MSe

– 2

(

– (

))

MSe

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(

– (

))

MSe

– 2

(

– (

))

MSe

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MSe

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MSe

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MSe

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MSe

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MSe

– 5

(

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MSe

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MSe

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MSe

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MSe

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