19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
time= bo+b1*time
The REG Procedure
Model: MOD1
Dependent Variable: time
Number of Observations Read
20
Number of Observations Used
20
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
Pr > F
1 112160947 112160947 4679.53 <.0001
Error
18
Corrected Total
19 112592378
Root MSE
431432
23968
154.81741 R-Square 0.9962
Dependent Mean 1485.18600 Adj R-Sq
Coeff Var
0.9960
10.42411
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Intercept
1 -67.83242 41.39842
-1.64 0.1187
distance
1
68.41 <.0001
0.18424
0.00269
1
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
time= bo+b1*time
500
400
300
200
Residual
100
0
-100
-200
-300
-400
-1000
0
1000
2000
3000
4000
Predicted Value
5000
6000
7000
8000
2
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
time= bo+b1*time
Obs distance gender
time
date LOG_distance LOG_TIME
LOF
pred
residual
1
100.0 M
9.58 18125
2.00000
0.98137
100.0
-49.41
58.988
2
100.0 F
10.49 10424
2.00000
1.02078
100.0
-49.41
59.898
3
200.0 M
19.19 18129
2.30103
1.28307
200.0
-30.98
50.174
4
200.0 F
21.34 10499
2.30103
1.32919
200.0
-30.98
52.324
5
400.0 M
43.18 14482
2.60206
1.63528
400.0
5.86
37.316
6
400.0 F
47.60
9410
2.60206
1.67761
400.0
5.86
41.736
7
800.0 M
101.01 18503
2.90309
2.00436
800.0
79.56
21.449
8
800.0 F
113.28
8607
2.90309
2.05415
800.0
79.56
33.719
9
1500.0 M
206.00 14074
3.17609
2.31387
1500.0
208.53
-2.530
10
1500.0 F
230.46 12307
3.17609
2.36260
1500.0
208.53
21.930
11
3000.0 M
440.67 13393
3.47712
2.64411
3000.0
484.89
-44.222
12
3000.0 F
486.11 12309
3.47712
2.68673
3000.0
484.89
1.218
13
5000.0 M
757.35 16222
3.69897
2.87930
5000.0
853.38
-96.026
14
5000.0 F
851.15 17689
3.69897
2.93001
5000.0
853.38
-2.226
15 10000.0 M
1577.53 16674
4.00000
3.19798 10000.0 1774.58 -197.053
16 10000.0 F
1771.78 12304
4.00000
3.24841 10000.0 1774.58
17 21097.5 M
3503.00 18342
4.32423
3.54444 21097.5 3819.20 -316.205
18 21097.5 F
3950.00 18676
4.32423
3.59660 21097.5 3819.20
19 42195.0 M
7439.00 17803
4.62526
3.87151 42195.0 7706.24 -267.241
20 42195.0 F
8125.00 15808
4.62526
3.90982 42195.0 7706.24
-2.803
130.795
418.759
3
19:14 Saturday, July 23, 2011
4
Linear regression log_time and lg-distance
SRL Fitted line Time distance
9900
8900
7900
6900
Predicted Value of time
5900
4900
3900
2900
1900
900
-100
0
5000
10000
15000
20000
25000
distance
30000
35000
40000
45000
50000
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
Lack of fit test
The GLM Procedure
Class Level Information
Class
LOF
gender
Levels Values
10 100 200 400 800 1500 3000 5000 10000 21097.5 42195
2 FM
Number of Observations Read
20
Number of Observations Used
20
5
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
Lack of fit test
The GLM Procedure
Dependent Variable: time
Source
DF
Model
Sum of
Squares Mean Square F Value
9 112232490.9
Error
10
359887.6
Corrected Total
19 112592378.4
12470276.8
Pr > F
346.50 <.0001
35988.8
R-Square Coeff Var Root MSE time Mean
0.996804 12.77328
Source
DF
189.7070
1485.186
Type I SS Mean Square F Value
Pr > F
distance
1 112160946.7 112160946.7 3116.56 <.0001
LOF
8
Source
DF
71544.2
8943.0
0.25 0.9699
Type III SS Mean Square F Value
distance
0
0.00000
.
LOF
8 71544.17785
8943.02223
.
Pr > F
.
0.25 0.9699
6
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
The REG Procedure
Model: MOD4
Dependent Variable: LOG_TIME
Number of Observations Read
20
Number of Observations Used
20
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
Pr > F
1 16.80824 16.80824 15741.6 <.0001
Error
18
Corrected Total
19 16.82746
Root MSE
0.01922
0.00107
0.03268 R-Square 0.9989
Dependent Mean 2.45856 Adj R-Sq
Coeff Var
0.9988
1.32910
Parameter Estimates
Parameter Standard
Estimate
Error t Value Pr > |t|
Variable
DF
Intercept
1
-1.21326
LOG_distance
1
1.10905
0.03016
-40.22 <.0001
0.00884 125.47 <.0001
7
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
Predicted value and confidence limits
Obs distance gender
time
date LOG_distance LOG_TIME
LOF
pred
lower
1
100.0 M
9.58 18125
2.00000
0.98137
100.0 1.00484 0.97606
2
100.0 F
10.49 10424
2.00000
1.02078
100.0 1.00484 0.97606
3
200.0 M
19.19 18129
2.30103
1.28307
200.0 1.33869 1.31446
4
200.0 F
21.34 10499
2.30103
1.32919
200.0 1.33869 1.31446
5
400.0 M
43.18 14482
2.60206
1.63528
400.0 1.67255 1.65233
6
400.0 F
47.60
9410
2.60206
1.67761
400.0 1.67255 1.65233
7
800.0 M
101.01 18503
2.90309
2.00436
800.0 2.00641 1.98929
8
800.0 F
113.28
8607
2.90309
2.05415
800.0 2.00641 1.98929
9
1500.0 M
206.00 14074
3.17609
2.31387
1500.0 2.30918 2.29362
10
1500.0 F
230.46 12307
3.17609
2.36260
1500.0 2.30918 2.29362
11
3000.0 M
440.67 13393
3.47712
2.64411
3000.0 2.64303 2.62738
12
3000.0 F
486.11 12309
3.47712
2.68673
3000.0 2.64303 2.62738
13
5000.0 M
757.35 16222
3.69897
2.87930
5000.0 2.88907 2.87212
14
5000.0 F
851.15 17689
3.69897
2.93001
5000.0 2.88907 2.87212
15 10000.0 M
1577.53 16674
4.00000
3.19798 10000.0 3.22293 3.20294
16 10000.0 F
1771.78 12304
4.00000
3.24841 10000.0 3.22293 3.20294
17 21097.5 M
3503.00 18342
4.32423
3.54444 21097.5 3.58252 3.55823
18 21097.5 F
3950.00 18676
4.32423
3.59660 21097.5 3.58252 3.55823
Obs
upper
residual back_mean back_upper back_lower
1 1.03362 -0.023472
10.11
10.80
9.46
2 1.03362
0.015938
10.11
10.80
9.46
3 1.36293 -0.055619
21.81
23.06
20.63
4 1.36293 -0.009499
21.81
23.06
20.63
5 1.69277 -0.037267
47.05
49.29
44.91
6 1.69277
0.005057
47.05
49.29
44.91
7 2.02352 -0.002042
101.49
105.57
97.56
8 2.02352
0.047747
101.49
105.57
97.56
9 2.32473
0.004690
203.79
211.22
196.62
10 2.32473
0.053418
203.79
211.22
196.62
11 2.65869
0.001080
439.58
455.71
424.01
12 2.65869
0.043701
439.58
455.71
424.01
13 2.90603 -0.009778
774.59
805.44
744.93
14 2.90603
0.040932
774.59
805.44
744.93
15 3.24292 -0.024953
1670.82
1749.52
1595.67
16 3.24292
0.025479
1670.82
1749.52
1595.67
17 3.60681 -0.038078
3824.00
4043.95
3616.02
18 3.60681
3824.00
4043.95
3616.02
0.014079
8
19:14 Saturday, July 23, 2011
Linear regression log_time and lg-distance
Predicted value and confidence limits
Obs distance gender
time
date LOG_distance LOG_TIME
LOF
pred
lower
19 42195.0 M
7439.00 17803
4.62526
3.87151 42195.0 3.91637 3.88754
20 42195.0 F
8125.00 15808
4.62526
3.90982 42195.0 3.91637 3.88754
Obs
upper
residual back_mean back_upper back_lower
19 3.94521 -0.044860
8248.49
8814.77
7718.59
20 3.94521 -0.006551
8248.49
8814.77
7718.59
9
19:14 Saturday, July 23, 2011
10
Linear regression log_time and lg-distance
10000
10000
9000
9000
8000
8000
7000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
0
5000
10000
15000
20000
25000
30000
distance
gender
F
M
35000
40000
45000
50000
back_mean
time
Fitted curve
19:14 Saturday, July 23, 2011
11
Linear regression log_time and lg-distance
Residual plot
Residual
0.06
0.05
0.04
0.03
0.02
0.01
0.00
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
1
2
3
Predicted Value of LOG_TIME
gender
F
M
4