nlsfit: Fit nonlinear models
In easynls: Easy Nonlinear Model
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
The function fit some nonlinear models
Usage
1
Arguments
data
data is a data.frame
The first column should contain the treatments (explanatory variable) and the remaining columns the response variables.
model
define the model
1 = "y~a+b*x" linear
2 = "y~a+b*x+c*x^2" quadratic
3 = "y ~ a + b * (x - c) * (x <= c)" linear plateau
4 = "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)" quadratic plateau
5 = "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)" two linear
6 = "y~a*exp(b*x)" exponential
7 = "y~a*(1+b*(exp(-c*x)))^-1" logistic
8 = "y~a*(1-b*(exp(-c*x)))^3" van bertalanffy
9 = "y~a*(1-b*(exp(-c*x)))" brody
10 = "y~a*exp(-b*exp(-c*x)" gompertz
11 = "y~(a*x^b)*exp(-c*x)" lactation curve
12 = "y ~ a + b * (1 - exp(-c * x))" ruminal degradation curve
13 = "y~(a/(1+exp(2-4*c*(x-e))))+(b/(1+exp(2-4*d*(x-e))))" logistic bi-compartmental
start
start iterations values of model
Value
Returns coefficients of the models, t test for coefficients, R squared, adjusted R squared, AIC, BIC and the maximum (or minimum) values of y and critical point of x
Author(s)
Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>
References
KAPS, M. and LAMBERSON, W. R. Biostatistics for Animal Science: an introductory text. 2nd Edition. CABI Publishing, Wallingford, Oxfordshire, UK, 2009. 504p.
See Also
nls, nls2
Examples
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# data represent weights of an Angus cow at ages from 8 to 108 months (Kaps and Lamberson, 2009)
weight=c(280,340,430,480,550,580,590,600,590,600)
age=c(8,12,24,36,48,60,72,84,96,108)
data1=data.frame(age, weight)
# linear
nlsfit(data1, model=1)
# quadratic
nlsfit(data1, model=2)
# linear plateau
nlsfit(data1, model=3)
# quadratic plateau
nlsfit(data1, model=4)
# two linear
nlsfit(data1, model=5, start=c(250,6,2,50))
# exponential
nlsfit(data1, model=6, start=c(250,0.05))
# logistic
nlsfit(data1, model=7, start=c(600,4,0.05))
# van bertalanffy
nlsfit(data1, model=8, start=c(600,2,0.05))
# brody
nlsfit(data1, model=9, start=c(600,4,0.05))
# gompertz
nlsfit(data1, model=10, start=c(600,4,0.05))
# describe the growth of Zagorje turkeys (Kaps and Lamberson, 2009)
weight=c(44,66,100,150,265,370,455,605,770)
age=c(1,7,14,21,28,35,42,49,56)
data2=data.frame(age,weight)
# two linear
nlsfit(data2, model=5, start=c(25,6,10,20))
# using segmented regression to estimate a plateau
# the requirement for the methionine will be estimated measurements of gain of turkey poults
#(Kaps and Lamberson, 2009)
methionine=c(80,85,90,95,100,105,110,115,120)
gain=c(102,115,125,133,140,141,142,140,142)
data3=data.frame(methionine, gain)
# linear
nlsfit(data3, model=1)
# quadratic
nlsfit(data3, model=2)
# linear plateau
nlsfit(data3, model=3)
# quadratic plateau
nlsfit(data3, model=4)
# lactation curve
milk=c(25,24,26,28,30,31,27,26,25,24,23,24,22,21,22,20,21,19,
18,17,18,18,16,17,15,16,14)
days=c(15,15,15,75,75,75,135,135,135,195,195,195,255,255,255,
315,315,315,375,375,375,435,435,435,495,495,495)
data4=data.frame(days,milk)
nlsfit(data4, model=11, start=c(16,0.25,0.004))
# ruminal degradation
time=c(2,6,9,24,48,72,96)
deg=c(20,33,46,55,66,72,76)
data5=data.frame(time,deg)
nlsfit(data5, model=12)
# logistic bi-compartmental (gas production)
time=c(0,12,24,36,48,60,72,84,96,108,120,144,168,192)
gas=c(0.002,3.8,8,14.5,16,16.5,17,17.4,17.9,18.1,18.8,
19,19.2,19.3)
data6=data.frame(time,gas)
nlsfit(data6, model=13, start=c(19,4,0.025,0.004,5))
Example output
$Model
[1] "y~a+b*x"
$Parameters
weight
coefficient a 339.4654
coefficient b 3.0025
p-value t.test for a 0.0000
p-value t.test for b 0.0004
r-squared 0.8035
adjusted r-squared 0.7789
AIC 112.3822
BIC 113.2899
$Model
[1] "y~a+b*x+c*x^2"
$Parameters
weight
coefficient a 232.7150
coefficient b 8.8342
coefficient c -0.0518
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9874
adjusted r-squared 0.9838
AIC 86.9145
BIC 88.1249
maximum or minimum value for y 609.5294
critical point in x 85.3082
$Model
[1] "y ~ a + b * (x - c) * (x <= c)"
$Parameters
weight
coefficient a 592.0000
coefficient b 6.3873
coefficient c 53.1548
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9869
adjusted r-squared 0.9831
AIC 87.3110
BIC 88.5213
maximum or minimum value for y 592.0000
critical point in x 53.1548
$Model
[1] "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)"
$Parameters
weight
coefficient a 216.0022
coefficient b 10.1285
coefficient c -0.0676
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9945
adjusted r-squared 0.9929
AIC 78.6308
BIC 79.8412
maximum or minimum value for y 595.1217
critical point in x 74.8622
$Model
[1] "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)"
$Parameters
weight
coefficient a 244.1667
coefficient b 6.9167
coefficient c -6.2262
coefficient d 46.0918
p-value t.test for a 0.0000
p-value t.test for b 0.0001
p-value t.test for c 0.0003
p-value t.test for d 0.0000
r-squared 0.9866
adjusted r-squared 0.9800
AIC 89.5001
BIC 91.0130
$Model
[1] "y~a*exp(b*x)"
$Parameters
weight
coefficient a 368.2618
coefficient b 0.0055
p-value t.test for a 0.0000
p-value t.test for b 0.0019
r-squared 0.7411
adjusted r-squared 0.7087
AIC 115.1412
BIC 116.0490
$Model
[1] "y~a*(1+b*(exp(-c*x)))^-1"
$Parameters
weight
coefficient a 602.8890
coefficient b 1.6953
coefficient c 0.0579
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9931
adjusted r-squared 0.9911
AIC 80.9263
BIC 82.1366
$Model
[1] "y~a*(1-b*(exp(-c*x)))^3"
$Parameters
weight
coefficient a 608.6197
coefficient b 0.3165
coefficient c 0.0444
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9929
adjusted r-squared 0.9908
AIC 81.2191
BIC 82.4294
$Model
[1] "y~a*(1-b*(exp(-c*x)))"
$Parameters
weight
coefficient a 612.8656
coefficient b 0.7272
coefficient c 0.0380
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9922
adjusted r-squared 0.9900
AIC 82.0835
BIC 83.2938
$Model
[1] "y~a*exp(-b*exp(-c*x)"
$Parameters
weight
coefficient a 606.9001
coefficient b 1.0915
coefficient c 0.0476
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9930
adjusted r-squared 0.9911
AIC 80.9729
BIC 82.1833
$Model
[1] "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)"
$Parameters
weight
coefficient a 38.2992
coefficient b 4.3228
coefficient c 12.8404
coefficient d 20.5018
p-value t.test for a 0.1891
p-value t.test for b 0.1811
p-value t.test for c 0.0070
p-value t.test for d 0.0018
r-squared 0.9938
adjusted r-squared 0.9900
AIC 88.6271
BIC 89.6133
$Model
[1] "y~a+b*x"
$Parameters
gain
coefficient a 38.7778
coefficient b 0.9233
p-value t.test for a 0.0771
p-value t.test for b 0.0016
r-squared 0.7793
adjusted r-squared 0.7478
AIC 64.7925
BIC 65.3841
$Model
[1] "y~a+b*x+c*x^2"
$Parameters
gain
coefficient a -377.1169
coefficient b 9.3822
coefficient c -0.0423
p-value t.test for a 0.0001
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9892
adjusted r-squared 0.9856
AIC 39.6409
BIC 40.4298
maximum or minimum value for y 143.1995
critical point in x 110.9156
$Model
[1] "y ~ a + b * (x - c) * (x <= c)"
$Parameters
gain
coefficient a 141.0000
coefficient b 2.0600
coefficient c 98.3010
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9937
adjusted r-squared 0.9916
AIC 34.7552
BIC 35.5441
maximum or minimum value for y 141.0000
critical point in x 98.3010
$Model
[1] "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)"
$Parameters
gain
coefficient a -474.4471
coefficient b 11.4890
coefficient c -0.0536
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9969
adjusted r-squared 0.9958
AIC 28.4725
BIC 29.2614
maximum or minimum value for y 141.4498
critical point in x 107.2147
$Model
[1] "y~(a*x^b)*exp(-c*x)"
$Parameters
milk
coefficient a 18.3409
coefficient b 0.1344
coefficient c 0.0022
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9396
adjusted r-squared 0.9345
AIC 90.9676
BIC 96.1510
maximum or minimum value for y 27.9360
critical point in x 62.2340
$Model
[1] "y ~ a + b * (1 - exp(-c * x))"
$Parameters
deg
coefficient a 17.4030
coefficient b 55.6709
coefficient c 0.0554
p-value t.test for a 0.0337
p-value t.test for b 0.0005
p-value t.test for c 0.0273
r-squared 0.9664
adjusted r-squared 0.9495
AIC 45.5423
BIC 45.3259
$Model
[1] "y~(a/(1+exp(2-4*c*(x-e))))+(b/(1+exp(2-4*d*(x-e))))"
$Parameters
gas
coefficient a 15.1675
coefficient b 4.3371
coefficient c 0.0362
coefficient d 0.0073
coefficient e 9.7433
p-value t.test for a 0.0000
p-value t.test for b 0.0004
p-value t.test for c 0.0000
p-value t.test for d 0.0047
p-value t.test for e 0.0001
r-squared 0.9955
adjusted r-squared 0.9934
AIC 26.1631
BIC 29.9974
easynls documentation built on May 2, 2019, 3:30 p.m.
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Description Usage Arguments Value Author(s) References See Also Examples
Description
The function fit some nonlinear models
Usage
1 |
Arguments
data |
data is a data.frame The first column should contain the treatments (explanatory variable) and the remaining columns the response variables. |
model |
define the model 1 = "y~a+b*x" linear 2 = "y~a+b*x+c*x^2" quadratic 3 = "y ~ a + b * (x - c) * (x <= c)" linear plateau 4 = "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)" quadratic plateau 5 = "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)" two linear 6 = "y~a*exp(b*x)" exponential 7 = "y~a*(1+b*(exp(-c*x)))^-1" logistic 8 = "y~a*(1-b*(exp(-c*x)))^3" van bertalanffy 9 = "y~a*(1-b*(exp(-c*x)))" brody 10 = "y~a*exp(-b*exp(-c*x)" gompertz 11 = "y~(a*x^b)*exp(-c*x)" lactation curve 12 = "y ~ a + b * (1 - exp(-c * x))" ruminal degradation curve 13 = "y~(a/(1+exp(2-4*c*(x-e))))+(b/(1+exp(2-4*d*(x-e))))" logistic bi-compartmental |
start |
start iterations values of model |
Value
Returns coefficients of the models, t test for coefficients, R squared, adjusted R squared, AIC, BIC and the maximum (or minimum) values of y and critical point of x
Author(s)
Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>
References
KAPS, M. and LAMBERSON, W. R. Biostatistics for Animal Science: an introductory text. 2nd Edition. CABI Publishing, Wallingford, Oxfordshire, UK, 2009. 504p.
See Also
nls, nls2
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | # data represent weights of an Angus cow at ages from 8 to 108 months (Kaps and Lamberson, 2009)
weight=c(280,340,430,480,550,580,590,600,590,600)
age=c(8,12,24,36,48,60,72,84,96,108)
data1=data.frame(age, weight)
# linear
nlsfit(data1, model=1)
# quadratic
nlsfit(data1, model=2)
# linear plateau
nlsfit(data1, model=3)
# quadratic plateau
nlsfit(data1, model=4)
# two linear
nlsfit(data1, model=5, start=c(250,6,2,50))
# exponential
nlsfit(data1, model=6, start=c(250,0.05))
# logistic
nlsfit(data1, model=7, start=c(600,4,0.05))
# van bertalanffy
nlsfit(data1, model=8, start=c(600,2,0.05))
# brody
nlsfit(data1, model=9, start=c(600,4,0.05))
# gompertz
nlsfit(data1, model=10, start=c(600,4,0.05))
# describe the growth of Zagorje turkeys (Kaps and Lamberson, 2009)
weight=c(44,66,100,150,265,370,455,605,770)
age=c(1,7,14,21,28,35,42,49,56)
data2=data.frame(age,weight)
# two linear
nlsfit(data2, model=5, start=c(25,6,10,20))
# using segmented regression to estimate a plateau
# the requirement for the methionine will be estimated measurements of gain of turkey poults
#(Kaps and Lamberson, 2009)
methionine=c(80,85,90,95,100,105,110,115,120)
gain=c(102,115,125,133,140,141,142,140,142)
data3=data.frame(methionine, gain)
# linear
nlsfit(data3, model=1)
# quadratic
nlsfit(data3, model=2)
# linear plateau
nlsfit(data3, model=3)
# quadratic plateau
nlsfit(data3, model=4)
# lactation curve
milk=c(25,24,26,28,30,31,27,26,25,24,23,24,22,21,22,20,21,19,
18,17,18,18,16,17,15,16,14)
days=c(15,15,15,75,75,75,135,135,135,195,195,195,255,255,255,
315,315,315,375,375,375,435,435,435,495,495,495)
data4=data.frame(days,milk)
nlsfit(data4, model=11, start=c(16,0.25,0.004))
# ruminal degradation
time=c(2,6,9,24,48,72,96)
deg=c(20,33,46,55,66,72,76)
data5=data.frame(time,deg)
nlsfit(data5, model=12)
# logistic bi-compartmental (gas production)
time=c(0,12,24,36,48,60,72,84,96,108,120,144,168,192)
gas=c(0.002,3.8,8,14.5,16,16.5,17,17.4,17.9,18.1,18.8,
19,19.2,19.3)
data6=data.frame(time,gas)
nlsfit(data6, model=13, start=c(19,4,0.025,0.004,5))
|
Example output
$Model
[1] "y~a+b*x"
$Parameters
weight
coefficient a 339.4654
coefficient b 3.0025
p-value t.test for a 0.0000
p-value t.test for b 0.0004
r-squared 0.8035
adjusted r-squared 0.7789
AIC 112.3822
BIC 113.2899
$Model
[1] "y~a+b*x+c*x^2"
$Parameters
weight
coefficient a 232.7150
coefficient b 8.8342
coefficient c -0.0518
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9874
adjusted r-squared 0.9838
AIC 86.9145
BIC 88.1249
maximum or minimum value for y 609.5294
critical point in x 85.3082
$Model
[1] "y ~ a + b * (x - c) * (x <= c)"
$Parameters
weight
coefficient a 592.0000
coefficient b 6.3873
coefficient c 53.1548
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9869
adjusted r-squared 0.9831
AIC 87.3110
BIC 88.5213
maximum or minimum value for y 592.0000
critical point in x 53.1548
$Model
[1] "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)"
$Parameters
weight
coefficient a 216.0022
coefficient b 10.1285
coefficient c -0.0676
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9945
adjusted r-squared 0.9929
AIC 78.6308
BIC 79.8412
maximum or minimum value for y 595.1217
critical point in x 74.8622
$Model
[1] "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)"
$Parameters
weight
coefficient a 244.1667
coefficient b 6.9167
coefficient c -6.2262
coefficient d 46.0918
p-value t.test for a 0.0000
p-value t.test for b 0.0001
p-value t.test for c 0.0003
p-value t.test for d 0.0000
r-squared 0.9866
adjusted r-squared 0.9800
AIC 89.5001
BIC 91.0130
$Model
[1] "y~a*exp(b*x)"
$Parameters
weight
coefficient a 368.2618
coefficient b 0.0055
p-value t.test for a 0.0000
p-value t.test for b 0.0019
r-squared 0.7411
adjusted r-squared 0.7087
AIC 115.1412
BIC 116.0490
$Model
[1] "y~a*(1+b*(exp(-c*x)))^-1"
$Parameters
weight
coefficient a 602.8890
coefficient b 1.6953
coefficient c 0.0579
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9931
adjusted r-squared 0.9911
AIC 80.9263
BIC 82.1366
$Model
[1] "y~a*(1-b*(exp(-c*x)))^3"
$Parameters
weight
coefficient a 608.6197
coefficient b 0.3165
coefficient c 0.0444
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9929
adjusted r-squared 0.9908
AIC 81.2191
BIC 82.4294
$Model
[1] "y~a*(1-b*(exp(-c*x)))"
$Parameters
weight
coefficient a 612.8656
coefficient b 0.7272
coefficient c 0.0380
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9922
adjusted r-squared 0.9900
AIC 82.0835
BIC 83.2938
$Model
[1] "y~a*exp(-b*exp(-c*x)"
$Parameters
weight
coefficient a 606.9001
coefficient b 1.0915
coefficient c 0.0476
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9930
adjusted r-squared 0.9911
AIC 80.9729
BIC 82.1833
$Model
[1] "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)"
$Parameters
weight
coefficient a 38.2992
coefficient b 4.3228
coefficient c 12.8404
coefficient d 20.5018
p-value t.test for a 0.1891
p-value t.test for b 0.1811
p-value t.test for c 0.0070
p-value t.test for d 0.0018
r-squared 0.9938
adjusted r-squared 0.9900
AIC 88.6271
BIC 89.6133
$Model
[1] "y~a+b*x"
$Parameters
gain
coefficient a 38.7778
coefficient b 0.9233
p-value t.test for a 0.0771
p-value t.test for b 0.0016
r-squared 0.7793
adjusted r-squared 0.7478
AIC 64.7925
BIC 65.3841
$Model
[1] "y~a+b*x+c*x^2"
$Parameters
gain
coefficient a -377.1169
coefficient b 9.3822
coefficient c -0.0423
p-value t.test for a 0.0001
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9892
adjusted r-squared 0.9856
AIC 39.6409
BIC 40.4298
maximum or minimum value for y 143.1995
critical point in x 110.9156
$Model
[1] "y ~ a + b * (x - c) * (x <= c)"
$Parameters
gain
coefficient a 141.0000
coefficient b 2.0600
coefficient c 98.3010
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9937
adjusted r-squared 0.9916
AIC 34.7552
BIC 35.5441
maximum or minimum value for y 141.0000
critical point in x 98.3010
$Model
[1] "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)"
$Parameters
gain
coefficient a -474.4471
coefficient b 11.4890
coefficient c -0.0536
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9969
adjusted r-squared 0.9958
AIC 28.4725
BIC 29.2614
maximum or minimum value for y 141.4498
critical point in x 107.2147
$Model
[1] "y~(a*x^b)*exp(-c*x)"
$Parameters
milk
coefficient a 18.3409
coefficient b 0.1344
coefficient c 0.0022
p-value t.test for a 0.0000
p-value t.test for b 0.0000
p-value t.test for c 0.0000
r-squared 0.9396
adjusted r-squared 0.9345
AIC 90.9676
BIC 96.1510
maximum or minimum value for y 27.9360
critical point in x 62.2340
$Model
[1] "y ~ a + b * (1 - exp(-c * x))"
$Parameters
deg
coefficient a 17.4030
coefficient b 55.6709
coefficient c 0.0554
p-value t.test for a 0.0337
p-value t.test for b 0.0005
p-value t.test for c 0.0273
r-squared 0.9664
adjusted r-squared 0.9495
AIC 45.5423
BIC 45.3259
$Model
[1] "y~(a/(1+exp(2-4*c*(x-e))))+(b/(1+exp(2-4*d*(x-e))))"
$Parameters
gas
coefficient a 15.1675
coefficient b 4.3371
coefficient c 0.0362
coefficient d 0.0073
coefficient e 9.7433
p-value t.test for a 0.0000
p-value t.test for b 0.0004
p-value t.test for c 0.0000
p-value t.test for d 0.0047
p-value t.test for e 0.0001
r-squared 0.9955
adjusted r-squared 0.9934
AIC 26.1631
BIC 29.9974
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