I was wondering why do I get linear model when I'm using exponential model,
y = a * exp(-b*-x)
, to fit my data.
Here is my code:
ff <- function(x,a,b){a * exp(-b*-x)}
fit2 <- nls(y ~ ff(x,a,b) , data = newdat, start =c(a=107.4623,b=-0.0037)
The graph below is mydata with the exponential fit (prediction of fit2
) in purple curve. The green curve is what I though it would be, it is Smooth.splines
fit.
Result from fit2
:
Nonlinear regression model
model: dif2 ~ ff(age, a, b)
data: newdat
a b
109.743680 -0.003793
residual sum-of-squares: 2585
Number of iterations to convergence: 2
Achieved convergence tolerance: 1.446e-06
Here is my data:
ID x y
1 18 106.47
1 19 100.35
1 20 97.4
1 21 101.03
1 22 100.3
1 23 99.06
1 24 100.81
2 18 101.95
2 19 100.69
2 20 100.89
3 14 105.87
3 15 107.44
3 16 103.05
3 17 104.86
3 18 101.86
3 19 101.48
3 20 102.77
3 21 99.63
3 22 100.21
3 23 101.28
3 24 98.77
3 25 99.91
4 17 102.42
4 18 101.85
4 19 101.31
5 18 101.24
5 19 102.27
5 20 100.03
5 21 101.53
6 20 98.08
6 21 101.2
6 22 103.16
6 23 98.3
6 24 102.21
6 25 100.18
6 27 95.28
6 28 102.05
6 29 100.72
6 30 101.4
7 13 111.3
7 14 106.55
7 15 103.23
7 16 102.31
7 17 101.11
7 18 101.52
7 19 100.14
8 18 101.05
8 19 98.15
8 20 100.55
8 21 101.62
8 22 101.04
8 23 98.22
9 18 102.87
9 19 101.46
9 20 101.07
9 21 101.32
10 20 101.93
10 21 101.73
10 22 100.24
11 19 99.75
11 20 101.35
11 21 99.34
11 22 100.12
12 18 103.34
12 19 109.52
12 20 106.98
12 21 105.21
12 22 98.87
12 23 103.81
12 24 100.38
12 25 100.12
12 26 99.7
12 27 101.16
12 28 99.02
12 29 100.15
12 30 97.32
13 13 116.43
13 14 111.75
13 15 107.42
13 16 103.5
13 17 103.37
13 18 100.66
13 19 100.73
13 20 100.84
13 21 100.05
14 18 101.66
14 19 99.9
14 20 101.4
14 21 99.86
14 22 100.82
15 15 101.27
15 16 100.01
15 17 104.27
16 19 100.26
16 20 104.13
17 18 106.12
18 21 101.18
18 22 99.51
18 23 100.59
19 18 100
19 19 100.81
19 20 99.37
19 21 102.6
20 22 102.18
20 23 104.5
20 24 100.74
21 22 103.74
21 23 98.66
21 24 100.65
21 25 99.63
22 24 102.59
22 25 94.62
22 26 103.85
23 20 100.7
23 21 101.38
23 22 102.36
23 23 99.56
23 24 100
24 18 101.16
24 19 99.64
25 21 96.9
25 22 109.3
25 23 101.4
25 24 98.04
25 25 99.28
25 26 99.63
25 27 101.29
25 28 100.08
26 14 109
26 15 112.37
26 16 102.4
26 17 102.15
26 18 100.82
27 18 101.14
27 19 101.38
28 17 105.09
28 18 101.74
28 19 100.2
29 19 102.11
29 20 100.57
29 21 100.91
29 22 99.61
29 23 99.99
30 18 99.81
30 19 102.07
31 19 100.75
31 21 95.43
32 23 99.73
32 24 100.8
32 25 100.1
32 26 100.88
32 27 97.73
32 28 100.36
33 22 99.4
33 24 101.46
33 18 97.65
33 25 102.75
33 26 97.7
33 27 100.67
34 21 98.27
34 22 100.42
34 23 101.16
34 24 100.13
34 25 98.55
35 17 107.46
35 18 100.22
35 19 102.03
35 20 101.52
35 21 102.05
35 22 102.46
35 23 101.56
35 24 96.88
35 25 98.97
35 26 101.68
35 28 94.12
36 20 98.63
36 21 101.59
36 22 98.76
37 19 101.9
37 20 98.66
37 21 100.19
37 22 100.03
37 23 99.97
38 15 104.32
38 16 102.98
38 17 103.4
38 18 102.78
38 19 101.73
38 20 95.57
39 22 101.5
39 23 98.37
39 24 100.4
39 25 100.79
40 19 102.93
40 20 100.88
40 21 99
40 22 99.66
41 21 107.08
41 22 93.08
41 24 100.91
41 25 107.24
41 26 99.8
42 14 109.82
42 15 106.09
42 16 106.32
42 17 102.8
42 18 100.21
42 19 102.08
42 21 99.22
42 22 100.13
42 23 101.63
43 16 100.95
43 17 100.6
43 18 101.81
43 19 102.78
43 20 98.43
43 23 101.4
43 24 103.12
43 25 99.31
43 26 100.47
43 27 99.67
43 28 98.75
43 29 95.68
44 23 103.78
44 24 100.38
44 25 99.39
44 26 100.87
44 27 99.64
44 28 98.39
44 29 97.62
45 18 100.47
45 19 101.41
45 20 99.33
45 21 101.08
45 22 100.08
45 23 100.22
45 24 99.67
45 25 100.45
45 26 102.4
45 27 95.7
46 20 101.35
46 21 98.73
46 22 109.29
46 23 100.04
46 24 95.74
46 25 100.44
46 26 98.72
47 19 100.51
47 20 99.88
47 21 101.7
47 22 101.94
47 23 100.72
47 24 98.73
47 25 102.16
47 26 100.25
47 27 95.1
47 28 103.08
48 25 105.21
48 26 100.48
48 27 98.07
48 28 99.88
48 29 95.61
49 16 111.35
49 17 92.43
49 18 112.04
49 19 100.8
49 20 95.36
49 21 103.13
49 22 102.16
49 23 98.81
49 25 98.86
49 26 99.93
49 27 95.26
50 23 98.15
50 24 105.93
50 25 99.01
50 26 99.34
50 27 93.68
50 28 105.35
51 24 100.96
51 25 100.53
51 26 99.2
51 27 100.52
51 28 100.86
52 25 101.38
52 26 98.45
52 27 100.32
52 28 99.24
52 29 102.74
53 24 101.37
53 25 99.75
53 27 96.31
53 28 100.67
54 22 98.09
54 23 100.55
54 24 100.25
54 25 101.54
54 26 98.48
54 27 102.76
54 28 98.5
54 30 99.85
55 22 103.87
55 23 94.37
55 24 105.12
56 18 101.23
56 19 99.26
56 20 102.63
56 21 100.75
56 23 101.5
56 24 99.14
56 27 95.11
57 16 107.57
57 17 101.75
57 18 107.18
57 19 100.23
57 20 105.48
57 21 103.1
57 22 100.45
57 23 99.28
57 24 100.52
57 25 98.69
58 27 103.13
58 28 97.86
58 29 101.33
58 30 98.33
58 32 102.14
58 34 94.47
58 35 98.29
59 19 97.6
59 20 98.93
59 22 101.35
59 23 93.88
60 20 99.62
60 22 97.36
60 23 102.94
60 24 98.98
60 25 99.47
61 18 100.15
61 19 101.92
61 20 101.34
61 21 98.87
61 22 97.68
61 23 99.92
61 24 100.78
61 25 98.21
62 20 102.7
62 21 99.7
62 22 100.17
62 23 99.62
62 24 100.59