JMP Analysis of Swimming Data
Fit Model:
Y: Time
Construct Model Effects: Highlight XA, XB, XC, XD – Macros – Full Factorial
Personality: Standard Least Squares
Emphasis: Minimal Report
Fit Model Output:
Parameter Estimates: Right Click – Make into data table
Delete row 1: Intercept
Tables – Sort – sort by – Estimate
Rename the last 3 columns;
i: put the values from 1 to 15
(i – 0.5)/15: Cols – Formula: (i – 0.5)/15
z – Score: Cols – Formula: Probability – Normal Quantile[(i – 0.5)/15)]
Add a column: Full Effect: Cols – Formula: Estimate*2
Term
XC
XB
XA*XC
XC*XD
XA*XB*XC*XD
XA*XD
XB*XC*XD
XA*XB*XC
XD
XA*XB*XD
XA*XC*XD
XB*XD
XA*XB
XB*XC
XA
Estimate
–2.598125
–0.653125
–0.310625
–0.134375
–0.014375
0.015625
0.018125
0.021875
0.025625
0.045625
0.048125
0.065625
0.101875
0.454375
0.666875
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
(i – 0.5)/15
0.03333333
0.1
0.16666667
0.23333333
0.3
0.36666667
0.43333333
0.5
0.56666667
0.63333333
0.7
0.76666667
0.83333333
0.9
0.96666667
z – Score
–1.8339146
–1.2815516
–0.9674216
–0.7279133
–0.5244005
–0.3406948
–0.167894
0
0.167894
0.34069483
0.52440051
0.72791329
0.96742157
1.28155157
1.83391464
Full Effect
–5.19625
–1.30625
–0.62125
–0.26875
–0.02875
0.03125
0.03625
0.04375
0.05125
0.09125
0.09625
0.13125
0.20375
0.90875
1.33375
Fit Y by X:
Y, Response: z – Score
X, Factor: Full Effect
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Fit Y by X Output:
Highlight the points you feel are most different from the rest (in upper right and lower left hand
corner that appear to be furthest from a straight line going through (0, 0) and capturing a majority
of the estimated full effects).
Rows – Exclude
Fit line
Bivariate Fit of z - Score By Full Effect
XA
XB*XC
XA*XC
XB
XC
Term
XA
XB
XC
XA*XC
XB*XC
Parameter Estimate
0.666875
–0.653125
–2.598125
–0.310625
0.454375
Full Effect
1.33375
–1.30625
–5.19625
–0.62125
0.90875
2
Full Model in 3 Factors: Pseudo Replication
Because XD is apparently not significant, either by itself or in combination with any other factor
of interaction, look at a reduced model. Fit a full factorial in XA, XB and XC.
Response: Time
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
Analysis of Variance
Source
DF Sum of Squares
Model
7
126.96559
Error
8
0.45115
C. Total
15
127.41674
Parameter Estimates
Term
Estimate
Intercept
19.706875
XA
0.666875
XB
–0.653125
XA*XB
0.101875
XC
–2.598125
XA*XC
–0.310625
XB*XC
0.454375
XA*XB*XC
0.021875
0.996459
0.993361
0.237474
19.70688
16
Mean Square
18.1379
0.0564
Std Error
0.059368
0.059368
0.059368
0.059368
0.059368
0.059368
0.059368
0.059368
t Ratio
331.94
11.23
–11.00
1.72
–43.76
–5.23
7.65
0.37
F Ratio
321.6304
Prob > F
<.0001*
Prob>|t|
<.0001*
<.0001*
<.0001*
0.1245
<.0001*
0.0008*
<.0001*
0.7221
Drop any terms that are not statistically significant to get the final prediction equation.
Predicted Time = 19.706875 + 0.666875*XA – 0.653125*XB – 2.598125*XC
– 0.310625*XA*XC + 0.454375*XB*XC
If you want to get the fastest (lowest) predicted time choose:
XA = –1, Wearing shirt? No
XB = +1, Wearing goggles? Yes
XC = +1, Wearing flippers? Yes
XD = –1 or +1, Starting End? It doesn’t matter.
Predicted Time = 19.706875 – 0.666875 – 0.653125 – 2.598125 + 0.310625 + 0.454375
Predicted Time = 16.55375 seconds.
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