Регрессионный анализ
I.I. Регрессионный анализ с помощью CurExpert 1.3
Linear Fit: y=a+bx
Coefficient Data:
a = 5.2901023
b = 0.64642075
Рис. 1. CurExpert 1.3. Уравнение прямой
Quadratic Fit: y=a+bx+cx^2
Coefficient Data:
a = 0.76099388
b = 1.3541632
c = -0.017469956
Рис. 2. CurExpert 1.3. Уравнение параболы
Exponential Association: y=a(1-exp(-bx)
Coefficient Data:
a = 29.841713
b = 0.056738502
Рис. 3. CurExpert 1.3. Уравнение экспоненциальной прямой
I.II. Регрессионный анализ с помощью Exel
Линии тренда для диаграмм типа графики (Exel)
Рис 4. Линии тренда для диаграмм типа графики
Рис 5. Линии тренда для диаграмм типа графики
I.III. Регрессионный анализ с помощью Table
Рис.6. Уравнение прямой с помощью Table
Данные о модели
Rank 41 Eqn 1 y=a+bx
r2 Coef Det DF Adj r2 Fit Std Err F-value
0.9142578857 0.8897601387 1.4131632259 85.303040879
Parm Value Std Error t-value 9 5% Confidence Limits
a 9.753737374 1.298089497 7.513917487 6.749886862 12.75758789
b 0.478989899 0.051861384 9.235964534 0.358979804 0.598999994
Area Xmin-Xmax Area Precision
567.27000000 4.892833e-19
Function min X-Value Function max X-Value
14.543644047 10.000016041 27.476363636 37.000000000
1st Deriv min X-Value 1st Deriv max X-Value
0.4789898990 22.858013550 0.4789898990 12.927609987
2nd Deriv min X-Value 2nd Deriv max X-Value
-1.1898e-09 15.006075332 5.948982e-10 36.629054365
Soln Vector Covar Matrix
Direct LUDecomp
r2 Coef Det DF Adj r2 Fit Std Err
0.9142578857 0.8897601387 1.4131632259
Source Sum of Squares DF Mean Square F
Regr 170.35276 1 170.35276 85.303
Error 15.976242 8 1.9970303
Total 186.329 9
X Variable:
Xmin: 10.000000000 Xmax: 37.000000000 Xrange: 27.000000000
Xmean: 23.500000000 Xstd: 9.0829510623 Xmedian: 23.500000000
X@Ymin: 10.000000000 X@Ymax: 37.000000000 X@Yrange: 27.000000000
Y Variable:
Ymin: 12.000000000 Ymax: 28.000000000 Yrange: 16.000000000
Ymean: 21.010000000 Ystd: 4.5500793644 Ymedian: 21.950000000
Y@Xmin: 12.000000000 Y@Xmax: 28.000000000 Y@Xrange: 16.000000000
Date Time File Source
Oct 24, 2012 3:27:20 PM
Rank 41 Eqn 1 y=a+bx
XY * X Value Y Value Y Predict Residual Residual% Confidence Limits Prediction Limits Weights
1 10.000000 12.000000 14.543636 -2.543636 -21.19697 12.621601 16.465672 10.750482 18.336791 1
2 13.000000 17.700000 15.980606 1.7193939 9.7140901 14.350500 17.610713 12.326698 19.634514 1
3 16.000000 17.700000 17.417576 0.2824242 1.5956172 16.046621 18.788530 13.871689 20.963463 1
4 19.000000 18.800000 18.854545 -0.054545 -0.290135 17.687914 20.021177 15.382539 22.326552 1
5 22.000000 21.500000 20.291515 1.2084848 5.6208598 19.241856 21.341175 16.857045 23.725985 1
6 25.000000 22.400000 21.728485 0.6715152 2.9978355 20.678825 22.778144 18.294015 25.162955 1
7 28.000000 23.500000 23.165455 0.3345455 1.4235977 21.998823 24.332086 19.693448 26.637461 1
8 31.000000 24.500000 24.602424 -0.102424 -0.418058 23.231470 25.973379 21.056537 28.148311 1
9 34.000000 24.000000 26.039394 -2.039394 -8.497475 24.409287 27.669500 22.385486 29.693302 1
10 37.000000 28.000000 27.476364 0.5236364 1.8701299 25.554328 29.398399 23.683209 31.269518 1
Рис 7. Уравнение параболы с помощью Table
Данные о модели
Rank 45 Eqn 1003 y=a+bx+cx2
r2 Coef Det DF Adj r2 Fit Std Err F-value
0.9327039969 0.8990559953 1.3383997358 48.509032283
Parm Value Std Error t-value 95% Confidence Limits
a 5.468636364 3.328871251 1.642789988 -2.43389353 13.37116625
b 0.900328283 0.308115690 2.922046209 0.168881115 1.631775450
c -0.00896465 0.006471819 -1.38518186 -0.02432834 0.006399043
Area Xmin-Xmax Area Precision
570.53761364 1.945924e-19
Function min X-Value Function max X-Value
13.575466112 10.000016041 26.508181818 37.000000000
1st Deriv min X-Value 1st Deriv max X-Value
0.2369444444 37.000000000 0.7210350659 10.000016041
2nd Deriv min X-Value 2nd Deriv max X-Value
-0.017929295 12.699154653 -0.017929291 13.731308268
Soln Vector Covar Matrix
Direct LUDecomp
r2 Coef Det DF Adj r2 Fit Std Err
0.9327039969 0.8990559953 1.3383997358
Source Sum of Squares DF Mean Square F
Regr 173.7898 2 86.894902 48.509
Error 12.539197 7 1.7913139
Total 186.329 9
X Variable:
Xmin: 10.000000000 Xmax: 37.000000000 Xrange: 27.000000000
Xmean: 23.500000000 Xstd: 9.0829510623 Xmedian: 23.500000000
X@Ymin: 10.000000000 X@Ymax: 37.000000000 X@Yrange: 27.000000000
Y Variable:
Ymin: 12.000000000 Ymax: 28.000000000 Yrange: 16.000000000
Ymean: 21.010000000 Ystd: 4.5500793644 Ymedian: 21.950000000
Y@Xmin: 12.000000000 Y@Xmax: 28.000000000 Y@Xrange: 16.000000000
Date Time File Source
Oct 24, 2012 3:48:10 PM
Rank 45 Eqn 1003 y=a+bx+cx2
XY * X Value Y Value Y Predict Residual Residual% Confidence Limits Prediction Limits Weights
1 10.000000 12.000000 13.575455 -1.575455 -13.12879 11.077336 16.073573 9.5337120 17.617197 1
2 13.000000 17.700000 15.657879 2.0421212 11.537408 13.980265 17.335492 12.064903 19.250854 1
3 16.000000 17.700000 17.578939 0.1210606 0.6839582 16.218511 18.939368 14.122662 21.035216 1
4 19.000000 18.800000 19.338636 -0.538636 -2.865087 17.933955 20.743318 15.864703 22.812570 1
5 22.000000 21.500000 20.936970 0.5630303 2.6187456 19.432395 22.441545 17.421457 24.452483 1
6 25.000000 22.400000 22.373939 0.0260606 0.1163420 20.869364 23.878515 18.858426 25.889452 1
7 28.000000 23.500000 23.649545 -0.149545 -0.636364 22.244864 25.054227 20.175612 27.123479 1
8 31.000000 24.500000 24.763788 -0.263788 -1.076685 23.403359 26.124216 21.307511 28.220065 1
9 34.000000 24.000000 25.716667 -1.716667 -7.152778 24.039053 27.394280 22.123691 29.309642 1
10 37.000000 28.000000 26.508182 1.4918182 5.3279221 24.010063 29.006301 22.466439 30.549924 1