Permodelan Matematis Kecepatan Kendaraan dengan metode Least Square
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BAB II
Tabel 2.1. Data hasil percobaan di lapangan :
NO X Y
1 1 38
2 2 39
3 3 41
4 4 40
5 5 42
6 6 39
7 7 41
8 8 36
9 9 39
10 10 43
11 11 46
12 12 41
Tabel 2.2.
NO X Y X^2 Y^2 XY
1 1 38 1 1444 38
2 2 39 4 1521 78
3 3 41 9 1681 123
4 4 40 16 1600 160
5 5 42 25 1764 210
6 6 39 36 1521 234
7 7 41 49 1681 287
8 8 36 64 1296 288
9 9 39 81 1521 351
10 10 43 100 1849 430
11 11 46 121 2116 506
12 12 41 144 1681 492
78 485 650 19675 3197
Untuk least square derajad 1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,435791333
R Square 0,189914086
Adjusted R Square 0,108905495
Standard Error 2,430406644
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 13,848 13,848 2,344 0,157
Residual 10 59,069 5,907
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 38,39393939 1,495811888 25,66762553 1,85035E-10
X 0,311188811 0,203240814 1,531133464 0,156736519
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 38,70512821 -0,705128205 -0,304288462
2 39,01631702 -0,016317016 -0,007041386
3 39,32750583 1,672494172 0,721742055
4 39,63869464 0,361305361 0,155916402
5 39,94988345 2,05011655 0,884699843
6 40,26107226 -1,261072261 -0,544198539
7 40,57226107 0,427738928 0,184584902
8 40,88344988 -4,883449883 -2,10738621
9 41,19463869 -2,194638695 -0,947066404
10 41,50582751 1,494172494 0,644789766
11 41,81701632 4,182983683 1,805109572
12 42,12820513 -1,128205128 -0,48686154
Untuk least square derajad 2 :
NO X X^2 Y
1 1 1 38
2 2 4 39
3 3 9 41
4 4 16 40
5 5 25 42
6 6 36 39
7 7 49 41
8 8 64 36
9 9 81 39
10 10 100 43
11 11 121 46
12 12 144 41
78 650 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,463962617
R Square 0,21526131
Adjusted R Square 0,040874935
Standard Error 2,521475086
Observations 12
ANOVA
df SS MS F Significance F
Regression 2 15,696 7,848 1,234 0,336
Residual 9 57,221 6,358
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 39,52272727 2,606017166 15,16595048 1,02525E-07
X -0,172577423 0,921689283 -0,187240348 0,855625265
X^2 0,037212787 0,069018938 0,539167772 0,60285136
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 39,38736264 -1,387362637 -0,608289614
2 39,32642358 -0,326423576 -0,143120527
3 39,33991009 1,66008991 0,727866978
4 39,42782218 0,572177822 0,250871558
5 39,59015984 2,40984016 1,056595226
6 39,82692308 -0,826923077 -0,3625647
7 40,13811189 0,861888112 0,377895132
8 40,52372627 -4,523726274 -1,983429302
9 40,98376623 -1,983766234 -0,86978297
10 41,51823177 1,481768232 0,649681778
11 42,12712288 3,872877123 1,698064273
12 42,81043956 -1,81043956 -0,793787832
Untuk least square derajad 3 :
NO X X^2 X^3 Y
1 1 1 1 38
2 2 4 8 39
3 3 9 27 41
4 4 16 64 40
5 5 25 125 42
6 6 36 216 39
7 7 49 343 41
8 8 64 512 36
9 9 81 729 39
10 10 100 1000 43
11 11 121 1331 46
12 12 144 1728 41
78 650 6084 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,533211893
R Square 0,284314923
Adjusted R Square 0,015933019
Standard Error 2,554049975
Observations 12
ANOVA
df SS MS F Significance F
Regression 3 20,731 6,910 1,059 0,418
Residual 8 52,185 6,523
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 36,67676768 4,178637818 8,777206658 2,22727E-05
X 2,027047027 2,672040355 0,758613927 0,46984097
X^2 -0,369352869 0,46800855 -0,789201115 0,452747001
X^3 0,020849521 0,023731154 0,878571713 0,405247493
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 38,35531136 -0,355311355 -0,163128952
2 39,42024642 -0,42024642 -0,192941647
3 39,99667 1,003330003 0,46064436
4 40,20967921 -0,20967921 -0,096266976
5 40,18437118 1,815628816 0,833583338
6 40,04584305 -1,045843046 -0,480162757
7 39,91919192 1,080808081 0,496215746
8 39,92951493 -3,92951493 -1,804101225
9 40,2019092 -1,201909202 -0,551815148
10 40,86147186 2,138528139 0,981831423
11 42,03330003 3,966699967 1,821173452
12 43,84249084 -2,842490842 -1,305031614
Untuk least square derajad 4 :
NO X X^2 X^3 X^4 Y
1 1 1 1 1 38
2 2 4 8 16 39
3 3 9 27 81 41
4 4 16 64 256 40
5 5 25 125 625 42
6 6 36 216 1296 39
7 7 49 343 2401 41
8 8 64 512 4096 36
9 9 81 729 6561 39
10 10 100 1000 10000 43
11 11 121 1331 14641 46
12 12 144 1728 20736 41
78 650 6084 60710 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,670788126
R Square 0,44995671
Adjusted R Square 0,135646259
Standard Error 2,393661965
Observations 12
ANOVA
df SS MS F Significance F
Regression 4 32,809 8,202 1,432 0,318
Residual 7 40,107 5,730
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 29,609 6,248 4,739 0,002
X 10,063 6,075 1,656 0,142
X^2 -2,902 1,799 -1,613 0,151
X^3 0,315 0,204 1,545 0,166
X^4 -0,011 0,008 -1,452 0,190
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 37,07371795 0,926282051 0,485096066
2 40,46882284 -1,468822844 -0,769225941
3 41,2782634 -0,278263403 -0,145727192
4 40,71454934 -0,71454934 -0,374211152
5 39,71833722 2,281662782 1,194912108
6 38,95843046 0,041569542 0,021770066
7 38,83177933 2,168220668 1,135502209
8 39,46348096 -3,463480963 -1,81383304
9 40,70677933 -1,706779332 -0,893844308
10 42,14306527 0,856934732 0,448778713
11 43,08187646 2,918123543 1,52822809
12 42,56089744 -1,560897436 -0,817445619
BAB II
Tabel 2.1. Data hasil percobaan di lapangan :
NO X Y
1 1 38
2 2 39
3 3 41
4 4 40
5 5 42
6 6 39
7 7 41
8 8 36
9 9 39
10 10 43
11 11 46
12 12 41
Tabel 2.2.
NO X Y X^2 Y^2 XY
1 1 38 1 1444 38
2 2 39 4 1521 78
3 3 41 9 1681 123
4 4 40 16 1600 160
5 5 42 25 1764 210
6 6 39 36 1521 234
7 7 41 49 1681 287
8 8 36 64 1296 288
9 9 39 81 1521 351
10 10 43 100 1849 430
11 11 46 121 2116 506
12 12 41 144 1681 492
78 485 650 19675 3197
Untuk least square derajad 1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,435791333
R Square 0,189914086
Adjusted R Square 0,108905495
Standard Error 2,430406644
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 13,848 13,848 2,344 0,157
Residual 10 59,069 5,907
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 38,39393939 1,495811888 25,66762553 1,85035E-10
X 0,311188811 0,203240814 1,531133464 0,156736519
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 38,70512821 -0,705128205 -0,304288462
2 39,01631702 -0,016317016 -0,007041386
3 39,32750583 1,672494172 0,721742055
4 39,63869464 0,361305361 0,155916402
5 39,94988345 2,05011655 0,884699843
6 40,26107226 -1,261072261 -0,544198539
7 40,57226107 0,427738928 0,184584902
8 40,88344988 -4,883449883 -2,10738621
9 41,19463869 -2,194638695 -0,947066404
10 41,50582751 1,494172494 0,644789766
11 41,81701632 4,182983683 1,805109572
12 42,12820513 -1,128205128 -0,48686154
Untuk least square derajad 2 :
NO X X^2 Y
1 1 1 38
2 2 4 39
3 3 9 41
4 4 16 40
5 5 25 42
6 6 36 39
7 7 49 41
8 8 64 36
9 9 81 39
10 10 100 43
11 11 121 46
12 12 144 41
78 650 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,463962617
R Square 0,21526131
Adjusted R Square 0,040874935
Standard Error 2,521475086
Observations 12
ANOVA
df SS MS F Significance F
Regression 2 15,696 7,848 1,234 0,336
Residual 9 57,221 6,358
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 39,52272727 2,606017166 15,16595048 1,02525E-07
X -0,172577423 0,921689283 -0,187240348 0,855625265
X^2 0,037212787 0,069018938 0,539167772 0,60285136
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 39,38736264 -1,387362637 -0,608289614
2 39,32642358 -0,326423576 -0,143120527
3 39,33991009 1,66008991 0,727866978
4 39,42782218 0,572177822 0,250871558
5 39,59015984 2,40984016 1,056595226
6 39,82692308 -0,826923077 -0,3625647
7 40,13811189 0,861888112 0,377895132
8 40,52372627 -4,523726274 -1,983429302
9 40,98376623 -1,983766234 -0,86978297
10 41,51823177 1,481768232 0,649681778
11 42,12712288 3,872877123 1,698064273
12 42,81043956 -1,81043956 -0,793787832
Untuk least square derajad 3 :
NO X X^2 X^3 Y
1 1 1 1 38
2 2 4 8 39
3 3 9 27 41
4 4 16 64 40
5 5 25 125 42
6 6 36 216 39
7 7 49 343 41
8 8 64 512 36
9 9 81 729 39
10 10 100 1000 43
11 11 121 1331 46
12 12 144 1728 41
78 650 6084 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,533211893
R Square 0,284314923
Adjusted R Square 0,015933019
Standard Error 2,554049975
Observations 12
ANOVA
df SS MS F Significance F
Regression 3 20,731 6,910 1,059 0,418
Residual 8 52,185 6,523
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 36,67676768 4,178637818 8,777206658 2,22727E-05
X 2,027047027 2,672040355 0,758613927 0,46984097
X^2 -0,369352869 0,46800855 -0,789201115 0,452747001
X^3 0,020849521 0,023731154 0,878571713 0,405247493
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 38,35531136 -0,355311355 -0,163128952
2 39,42024642 -0,42024642 -0,192941647
3 39,99667 1,003330003 0,46064436
4 40,20967921 -0,20967921 -0,096266976
5 40,18437118 1,815628816 0,833583338
6 40,04584305 -1,045843046 -0,480162757
7 39,91919192 1,080808081 0,496215746
8 39,92951493 -3,92951493 -1,804101225
9 40,2019092 -1,201909202 -0,551815148
10 40,86147186 2,138528139 0,981831423
11 42,03330003 3,966699967 1,821173452
12 43,84249084 -2,842490842 -1,305031614
Untuk least square derajad 4 :
NO X X^2 X^3 X^4 Y
1 1 1 1 1 38
2 2 4 8 16 39
3 3 9 27 81 41
4 4 16 64 256 40
5 5 25 125 625 42
6 6 36 216 1296 39
7 7 49 343 2401 41
8 8 64 512 4096 36
9 9 81 729 6561 39
10 10 100 1000 10000 43
11 11 121 1331 14641 46
12 12 144 1728 20736 41
78 650 6084 60710 485
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,670788126
R Square 0,44995671
Adjusted R Square 0,135646259
Standard Error 2,393661965
Observations 12
ANOVA
df SS MS F Significance F
Regression 4 32,809 8,202 1,432 0,318
Residual 7 40,107 5,730
Total 11 72,917
Coefficients Standard Error t Stat P-value
Intercept 29,609 6,248 4,739 0,002
X 10,063 6,075 1,656 0,142
X^2 -2,902 1,799 -1,613 0,151
X^3 0,315 0,204 1,545 0,166
X^4 -0,011 0,008 -1,452 0,190
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 37,07371795 0,926282051 0,485096066
2 40,46882284 -1,468822844 -0,769225941
3 41,2782634 -0,278263403 -0,145727192
4 40,71454934 -0,71454934 -0,374211152
5 39,71833722 2,281662782 1,194912108
6 38,95843046 0,041569542 0,021770066
7 38,83177933 2,168220668 1,135502209
8 39,46348096 -3,463480963 -1,81383304
9 40,70677933 -1,706779332 -0,893844308
10 42,14306527 0,856934732 0,448778713
11 43,08187646 2,918123543 1,52822809
12 42,56089744 -1,560897436 -0,817445619
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