a statistical analysis example of a full functional utilization of an engineering calculator li-fei...
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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
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).