A Statistical Analysis Example of A Full Functional Utilization of An Engineering Calculator

A Statistical Analysis Example of A Full Functional Utilization of

An Engineering Calculator

Li-Fei Huang ([email protected])

Dept. of App. Statistics & Info. Sci.

Ming Chuan University, TAIWAN

Outline

• Introduction

• Steps of simple linear regression analysis

• Commands for programming

• Regression test program

• Execution result

• Conclusions

• References

Introduction

• The functions and commands of statistical software which is installed in the computer are quite COMPLICATED.

• The engineering calculator is EASIER to manipulate and CHEAPER to possess. Today even the PROGRAMMING can be done.

• This paper will use CASIO fx-7400G PLUS to do the simple linear regression analysis.

CASIO fx-7400G PLUS

• The slope, the intercept and the coefficient of correlation are shown directly.

• There are NO further results about hypothesis testing.

• Lots of basic statistics such as can be extracted

from the memory of the calculator to create the program about hypothesis testing.

xyyxyxn ,,,,, 22

Simple linear regression (Step 1)

• The sum of squares for X:• The slope for the regression line: The intercept for the regression line:

2

1

2 )()( nxnxxSSXn

ii

SSX

yxnxyb

1

xbyb 10


• The sum of squares for regression:

• The sum of squares for Y or the sum of squares for total:

• The sum of squares for error:• The mean squares for error:• The regression F test value:

SSXbyySSRn

ii

21

1

2ˆ

2

1

2 )()( nynyySSTSSYn

ii

SSRSSTSSE

2

n

SSEMSE

MSE

SSR

nSSE

SSRF

)2(

1


• The coefficient of determination:• The coefficient of correlation: if X and Y are positively correlated, if X and Y are negatively correlated.

SST

SSRR 2

2R

2R


• The t tests for the slope and the intercept:

• The confidence interval and the prediction interval for a given value of X:

SSX

MSE

bt 11

nSSX

xMSE

bt

2

00

SSX

xX

nMSEtY

2

2

)(1ˆ

SSX

xX

nMSEtY

2

2

)(11ˆ

Commands for programming

• Parts of commands from CASIO fx-7400G PLUS manual:

Basic operation

Program command

Jump command

Display command ""

:

?

LblGoto

IfEndElseThenIf

Key-in a value.

Show calculation result.

Connect 2 commands.

Connect 2 commands.

Store result in A to Z.

An if-then-else loop.

Go to the label.

Show words in quotes.

Regression test program (Step1)

4

32

3

1

)

()(

1,2,1

2

2

tsiL

tsiLtsiL

ts

iLABtsiL

AxBy

Bnxn

yxnyx

tsiLts

iLelbairaV

TSETGER

Name the program.

Compute basic statistics of 2

variables.

Use basic statistics to find the slope

and store it in B.

Store the intercept in A.

Store Y hats in List 3.

Store residuals in List 4.


2:",1"

:""

:""

)2(

:""

:""

:""2

22

nFD

FF

FER

EESM

EnE

TTSS

EESS

ERT

Tnyn

RRSS

RnxnB

Store sum of squares for regression

in R and show it.

Store SST in T.

Store SSE in E.

Show SSE.

Show SST.

Store mean squares for error in E

and show it.

Store the F test value in F and

show it.

Show 2 degrees of freedom.


dnEfI

RReslE

RR

nehTBfI

RR

RTR

:""

:"

"0

:"" 2

Store and show the coefficient of

determination.

Find the coefficient of correlation

and show it.


• The t tests for the slope and the intercept:

T

TTPECRETNI

Tnxn

xEIA

IATEB

T

SETTEPOLS

Tnx

nESB

S

ATEBlbL

:

""

))

(()(

?"0"

:

""

))

(()(

?"

1":0

222

2

Put label 0 here.

Ask for a slope to test.

Store the slope t test value in T.

Show the slope t test value.

Ask for an intercept to test.

Store the intercept t test value in

T.

Show the intercept t test value.


• The SE parts of the confidence interval and the prediction interval for a given value of X:

0

:")("

))1((

:")("

)

)(1(

?""

2

2

2

otoG

HDERPES

HGE

EG

TAHYES

Gnxn

xXn

XXWEN

Ask for a new X value.

Compute and show the standard

error for Y hat.

Compute and show the standard

error for the prediction interval.

Go to label 0 and test another

slope.

Execution result

• One data set in the book of Berenson, Levine, & KrehbielNo. 1 2 3 4 5 6 7 8 9 10 11 12

X 5 5 5 10 10 10 15 15 15 20 20 20

Y 160 220 140 190 240 260 230 270 280 260 290 310

Execution result (Step 2)

01

,1

19665836.12

949

52003

0949

53502

FD

F

ESM

TSS

ESS

RSS

Press EXE to move on.







8936000728.0

3850039386.0

2

R

R




psiD

DERPES

TAHYES

XWEN

TTPECRETNI

ATEB

TSETTEPOLS

ATEB

69892927.73

)(

19020387.12

)(

52

?

856065656.6

0

?0

403727156.4

0

?1

Key-in the number.


Key-in the number.


Key-in the number.


Press EXE to move on or

press AC to stop program.

Conclusion 1

• This particular calculator can produce some built in graphs such as histogram, bar chart, pie chart, line chart, box-and-whisker plot, standard normal probability density function, linear regression line, quadratic regression line, log regression line, exponential regression line and power regression line.

Conclusion 2

• Using List 4 in previous example, residual plots can be produced to check whether this data set is suitable for regression analysis or not.

Conclusion 3

• Using basic statistics, the following tests besides the regression test can also be fulfilled: z test, one-sample t test, two-sample t test, paired t test, chi-square test for single variance and F test for two variances.

Conclusion 4

• Using the built in permutation and combination functions, the probability mass function and cumulative mass function for the following discrete probability distributions can be found: binomial distribution, hyper-geometric distribution, geometric distribution, Poisson distribution and negative binomial distribution.

Conclusion 5

• The built in list function can help doing many other analyses such as one way ANOVA, randomized block design, chi-square test for K╳ 1 table, chi-square test for R╳ C table, Wilcoxon rank sum test, etc.

• Generally speaking, this particular engineering calculator can accomplish lots of interesting statistical analyses if it’s fully utilized.

References

• CASIO fx-7400G PLUS manual.• Berenson, Levine, & Krehbiel. Basic Business

Statistics—Concepts and applications. Pearson International (Edition 11).

The End

• Thank you for your watching!

Documents

A Statistical Analysis Example of A Full Functional Utilization of An Engineering Calculator