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
n, x, y, x 2 , y 2 , xy can be extracted
from the memory of the calculator to create
the program about hypothesis testing.
Simple linear regression (Step 1)
n
• The sum of squares for X: SSX   ( x
• The slope for the regression line:
i 1
i
b1
 x ) 2  n( x 
xy  nx y


SSX
The intercept for the regression line: b0  y  b1 x
n) 2
Simple linear regression (Step 2)
• The sum of squares for regression:
n
SSR    yˆ i  y   b12 SSX
2
i 1
• The sum of squares for Y or the sum of
squares for total: SSY  SST   ( y  y )  n( yn)
• The sum of squares for error: SSE  SST  SSR
• The mean squares for error: MSE  nSSE
2
• The regression F test value: F  SSR 1  SSR
n
2
i 1
2
i
SSE (n  2)
MSE
Simple linear regression (Step 3)
SSR
SST
• The coefficient of determination:
• The coefficient of correlation:
R if X and Y are positively correlated,
 R if X and Y are negatively correlated.
R2 
2
2
Simple linear regression (Step 4)
• The t tests for the slope and the intercept:
t
b1  1
t
b0   0
MSE
MSE x 2
SSX
nSSX
• The confidence interval and the prediction
interval for a given value of X:
Yˆ  t
2
1 ( X  x)2
MSE

n
SSX
Yˆ  t
2
1 ( X  x)2
MSE 1  
n
SSX
Commands for programming
• Parts of commands from CASIO fx-7400G PLUS
manual:
Basic operation
?

Key-in a value.
Show calculation result.
Connect 2 commands.
:


Program command
Jump command
Display command
If Then Else IfEnd
Goto Lbl
"
"
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)

R E G
2
 V
a r i a b l e
s

t
1 , L i s t
(

x
n
y


x  n 2 )  B 
B  x  A 
L
i
s
s
t
L i
 L
T
E
y  n  x 
t

S T
1  B 
Name the program.
L i
Compute
2 , 1
variables.
y )  (
Use basic statistics to find the slope
Store the intercept in A.
A  L i
2  L i s t
4 
statistics of 2
and store it in B.
3 
s t
i s t
basic
3
Store Y hats in List 3.
Store residuals in List 4.
Regression test program (Step2)
B 2
" S
n 
T 
" S
" S
 n  x 
S
R  " :
y  n 2 
R  E 
S E  " :
S T  " :
E
"

M
(
S
R

E  F
"
"
F
D
n 2  R 
R 
T 
E 
T 
n  2 )  E 
E  " : E 

 " : F 
F  1 , " : n  2 
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)
R
 T
 R 
"
R
I
f
R

" :
E
l
s e
f
E n d
 " : R 
2
B  0
h e n
"
R 
" R  " : 

I
T

R
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:
L
b
l
"
?

(
B

0 : " B
S
S
E T

)  (
( E
2
x  n
) )  T 
" S L O P E
T T E
: T 
" B E
( A 
2
Put label 0 here.
A 1 
 n 
Show the slope t test value.
S
 "
Ask for an intercept to test.
T A 0  " ?  I 
I )  (
( E   x

n
I
T
N T

2
 x 
n
E
E
2
Ask for a slope to test.
Store the slope t test value in T.
Store the intercept t test value in
) )  T
T.

"
:
R C
P T
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:
"
n
"
G
N
(

S

(
S
E W
X  " ?  X 
1
 n  ( X  x ) 2 
x  n 2 )  G 
E
( Y
H A T )  " :
E
E
"

G o t o
E 
( 1  G
( P R E
0
Ask for a new X value.
Compute and show the standard
error for Y hat.
2
) )  H 
D )  " : H
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,
& Krehbiel
No.
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)
S
S
S
M
F
S
S
S
S
R 
E
T
E
2 0 5 3 5
Press EXE to move on.
9 4 9 0
Press EXE to move on.
3 0 0 2 5
Press EXE to move on.
9 4 9
Press EXE to move on.




D F
2
1 . 6 3 8 5 6 6 9 1

1 ,
1 0
Press EXE to move on.
Press EXE to move on.
Execution result (Step 3)

0 . 6 8 3 9 3 0 0 5 8 3
R 
0 . 8 2 7 0 0 0 6 3 9 8
R
2
Press EXE to move on.
Press EXE to move on.
Execution result (Step 4)
B E T
A 1  ?
0
S L O P E
T T E S T
4
. 6 5 1 7 2 7 3 0 4
B E T
A 0  ?
0
I N T E R C E P T
T
6
. 6 5 6 5 6 0 6 5 8
N E W
X  ?
2
S
S
5
E
E
Key-in the number.
Press EXE to move on.
Key-in the number.
Press EXE to move on.
Key-in the number.
(
2
Y
H A T ) 
1 . 7 8 3 0 2 0 9 1
( P R E D ) 
3 7 . 7 2 9 2 9 8 9 6

D i s p

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, hypergeometric 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!