A Statistical Analysis Example of A Full Functional Utilization of

An Engineering Calculator

Li-Fei Huang (lhuang@mcu.edu.tw)

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

Simple linear regression (Step 2)

• 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

Simple linear regression (Step 3)

• 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

Simple linear regression (Step 4)

• 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.

Regression test program (Step2)

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.

Regression test program (Step3)

dnEfI

RReslE

RR

nehTBfI

RR

RTR

:""

:"

"0

:"" 2

Store and show the coefficient of

determination.

Find the coefficient of correlation

and show it.

Regression test program (Step4)

• 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.

Regression test program (Step4)

• 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.

Press EXE to move on.

Press EXE to move on.

Press EXE to move on.

Press EXE to move on.

Press EXE to move on.

Execution result (Step 3)

8936000728.0

3850039386.0

2

R

R

Press EXE to move on.

Press EXE to move on.

Execution result (Step 4)

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.

Press EXE to move on.

Key-in the number.

Press EXE to move on.

Key-in the number.

Press EXE to move on.

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!