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( yn)
• 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!
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