Started statistics lecture

This commit is contained in:
2015-10-15 18:18:56 +02:00
parent 78ce93cb37
commit 06016d3e2f
149 changed files with 1015 additions and 0 deletions

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DOTSOURCES = $(wildcard figs/*.dot)
all: $(DOTSOURCES:dot=pdf)
pdflatex lecture_statistics*.tex
pdflatex lecture_statistics*.tex
pdflatex lecture_statistics*.tex
figs/prob%.pdf : figs/prob%.dot
dot -Tpdf -o $@ $<
figs/test%.pdf : figs/test%.dot
dot -Tpdf -o $@ $<
figs/fig%.pdf : figs/fig%.dot
dot -Tpdf -o $@ $<
clean:
rm -rf *.dvi *.pdf *.aux *.out *.log auto *.nav *.snm *.toc *.vrb

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all:
for number in 001 002 003 004 005 006 007 007 009 010 011 012 013 014 015 016 017 ; do \
echo $$number ; \
sed "s/000/$$number/g" day1.tex > tmp.tex; \
pdflatex tmp.tex; \
mv tmp.pdf day1_$$number.pdf; \
cp ../data/example$$number.csv ./ ;\
rm tmp.* ; \
zip example$$number.zip example$$number.csv day1_$$number.pdf ; \
rm example$$number.csv ;\
rm day1_$$number.pdf ; \
done
clean:
rm *.zip
rm -rf auto

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\documentclass[addpoints,10pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{afternoon assignment day 01}{10/20/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
\shadedsolutions
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question To publish scientific results, you will usually need to
use statistical methods. Some journals provide you with a brief
description of how they expect you to apply statistical methods. One
example can be found in the author guidelines of the journal
Nature.
Assume you collected the following dataset. You can download it from
Ilias as {\tt example000.csv}. Here is the description of the dataset:
\begin{quotation}
\tt
\input{../examples/example000.tex}
\end{quotation}
\begin{parts}
\part Download the dataset and write a script that loads it into
matlab.
\part Think about the type of your data (I might ask you that
tomorrow).
\part Produce a plot that displays the data in an appropriate
way. Make sure to respect all elements of good plotting we
discussed today.
\part Download the statistical checklist from nature. Produce {\bf
one} slide that contains the plot and a concise summary of your
data which respects the requirements made by nature (assume you
are producing a figure legend for the figure in nature). It is
good style to avoid expressions like ``the plot shows'' or
similar.
\part Upload your code, the data, and the slide as a zip to
Ilias. Deadline is 19h00. Structure the zip such that you can
present you program in front of the class. Several students will
be asked to present their slide and their code tomorrow morning.
\end{parts}
\end{questions}
\end{document}

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\documentclass[addpoints,10pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{afternoon assignment day 02}{10/21/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
\shadedsolutions
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question Download example002 from yesterday (brain weights).
\begin{parts}
\part Simulate a null distribution via permutation.
\part Determine whether you can reject ``means are equal'' on a
5\% significance level using the simulated null distribution.
\part Check whether the means are different with a two sample
t-test in matlab ({\tt ttest2}).
\part Plot the data appropriately and generate a single slide that
contains the plot and short discussion of the test that respects
the nature statistical checklist (ignore all question whether the
assumptions of the test are satisfied).
\part Upload the slide and the code to Ilias. Deadline is 19h00.
\end{parts}
\end{questions}
\end{document}

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\documentclass[addpoints,10pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{afternoon assignment day 02}{10/22/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
%\printanswers
\shadedsolutions
\begin{document}
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
\sffamily
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question When the p-value is small, we reject the null
hypothesis. For example, if you want to test whether two means are
not equal, the null hypothesis is ``means are equal''. If e.g. $p\le
0.05$ then we take it as sufficient evidence that the null
hypothesis is not true. Therefore, we assume that the means are not
equal (which is what you want to show).
In this exercise we will look at what kind of p-values we expect if
the null hypothesis is true. In our example, this would be the case
if the true means of two datasets are actually equal.
\begin{parts}
\part Think about how you expect the p-values to behave in that
situation.
\part Simulate the situation in which the means are equal by
repeating the following at least $1000$ times:
\begin{enumerate}
\item Generate two arrays {\tt x} and {\tt y} with $10$ normally
(Gaussian) distributed random numbers using {\tt randn}. By
construction, the true means behind the random number are zero.
\item Perform a two sample t-test ({\tt ttest2}) on {\tt x} and
{\tt y}. Store the p-value.
\end{enumerate}
\part Plot a histogram of the $1000$ p-values. What do you think
is the distribution the p-values (i.e. if you repeated this
experiment many more times, how would the histogram look like)?
\part Given what you find, think about whether the following
strategy is statistically valid: You collect $10$ data points from
each group and perform a test. If the test is not significant, you
collect $10$ more and repeat the test. If the test tells you that
there is a significant difference you stop. Otherwise you repeat
the procedure until the test is significant.
\end{parts}
\end{questions}
\end{document}

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../latex/beamercolorthemetuebingen.sty

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1607 0
1157 0
1248 0
1310 0
1398 0
1237 0
1232 0
1343 0
1380 0
1274 0
1245 0
1286 0
1508 0
1105 0
1123 0
1198 0
1300 0
1249 0
1185 0
915 0
1345 0
1107 0
1357 0
1227 0
1205 0
1435 0
1289 0
1093 0
1211 0
1260 0
1193 0
1330 0
1130 0
1357 0
1193 0
1232 0
1321 0
1260 0
1380 0
1230 0
1136 0
1029 0
1223 0
1240 0
1264 0
1020 0
1415 0
1410 0
1275 0
1230 0
1085 0
1048 0
1181 0
1103 0
1165 0
1547 0
1173 0
1660 0
1307 0
1535 0
1315 0
1257 0
1424 0
1309 0
1170 0
1412 0
1270 0
1230 0
1233 0
1561 0
1193 0
1272 0
1355 0
1137 0
1354 0
1110 0
1265 0
1407 0
1227 0
1330 0
1222 0
1305 0
1475 0
1177 0
1337 0
1145 0
1070 0
1305 0
1085 0
1303 0
1390 0
1532 0
1238 0
1233 0
1280 0
1245 0
1459 0
1157 0
1302 0
1385 0
1310 0
1342 0
1303 0
1248 0
1115 0
1365 0
1227 0
1353 0
1125 1
1027 1
1112 1
983 1
1090 1
1247 1
1045 1
983 1
972 1
1045 1
937 1
1245 1
1200 1
1270 1
1200 1
1145 1
1090 1
1040 1
1343 1
1010 1
1095 1
1180 1
1168 1
1095 1
1040 1
1235 1
1050 1
1038 1
1046 1
1255 1
1228 1
1000 1
1225 1
1220 1
1085 1
1067 1
1006 1
1138 1
1175 1
1252 1
1037 1
958 1
1020 1
1068 1
1107 1
1317 1
952 1
1056 1
1203 1
1183 1
1392 1
1130 1
1284 1
996 1
1228 1
1087 1
1035 1
1170 1
1064 1
1250 1
1129 1
1088 1
1037 1
1117 1
1095 1
1027 1
1027 1
1190 1
1153 1
1037 1
1120 1
1212 1
1024 1
1135 1
1177 1
1096 1
1114 1

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MAO,Diagnosis
6.8,I
4.1,I
7.3,I
14.2,I
18.8,I
9.9,I
7.4,I
11.9,I
5.2,I
7.8,I
7.8,I
8.7,I
12.7,I
14.5,I
10.7,I
8.4,I
9.7,I
10.6,I
7.8,II
4.4,II
11.4,II
3.1,II
4.3,II
10.1,II
1.5,II
7.4,II
5.2,II
10,II
3.7,II
5.5,II
8.5,II
7.7,II
6.8,II
3.1,II
6.4,III
10.8,III
1.1,III
2.9,III
4.5,III
5.8,III
9.4,III
6.8,III
1 MAO Diagnosis
2 6.8 I
3 4.1 I
4 7.3 I
5 14.2 I
6 18.8 I
7 9.9 I
8 7.4 I
9 11.9 I
10 5.2 I
11 7.8 I
12 7.8 I
13 8.7 I
14 12.7 I
15 14.5 I
16 10.7 I
17 8.4 I
18 9.7 I
19 10.6 I
20 7.8 II
21 4.4 II
22 11.4 II
23 3.1 II
24 4.3 II
25 10.1 II
26 1.5 II
27 7.4 II
28 5.2 II
29 10 II
30 3.7 II
31 5.5 II
32 8.5 II
33 7.7 II
34 6.8 II
35 3.1 II
36 6.4 III
37 10.8 III
38 1.1 III
39 2.9 III
40 4.5 III
41 5.8 III
42 9.4 III
43 6.8 III

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Weight,Sex
1607,m
1157,m
1248,m
1310,m
1398,m
1237,m
1232,m
1343,m
1380,m
1274,m
1245,m
1286,m
1508,m
1105,m
1123,m
1198,m
1300,m
1249,m
1185,m
915,m
1345,m
1107,m
1357,m
1227,m
1205,m
1435,m
1289,m
1093,m
1211,m
1260,m
1193,m
1330,m
1130,m
1357,m
1193,m
1232,m
1321,m
1260,m
1380,m
1230,m
1136,m
1029,m
1223,m
1240,m
1264,m
1020,m
1415,m
1410,m
1275,m
1230,m
1085,m
1048,m
1181,m
1103,m
1165,m
1547,m
1173,m
1660,m
1307,m
1535,m
1315,m
1257,m
1424,m
1309,m
1170,m
1412,m
1270,m
1230,m
1233,m
1561,m
1193,m
1272,m
1355,m
1137,m
1354,m
1110,m
1265,m
1407,m
1227,m
1330,m
1222,m
1305,m
1475,m
1177,m
1337,m
1145,m
1070,m
1305,m
1085,m
1303,m
1390,m
1532,m
1238,m
1233,m
1280,m
1245,m
1459,m
1157,m
1302,m
1385,m
1310,m
1342,m
1303,m
1248,m
1115,m
1365,m
1227,m
1353,m
1125,f
1027,f
1112,f
983,f
1090,f
1247,f
1045,f
983,f
972,f
1045,f
937,f
1245,f
1200,f
1270,f
1200,f
1145,f
1090,f
1040,f
1343,f
1010,f
1095,f
1180,f
1168,f
1095,f
1040,f
1235,f
1050,f
1038,f
1046,f
1255,f
1228,f
1000,f
1225,f
1220,f
1085,f
1067,f
1006,f
1138,f
1175,f
1252,f
1037,f
958,f
1020,f
1068,f
1107,f
1317,f
952,f
1056,f
1203,f
1183,f
1392,f
1130,f
1284,f
996,f
1228,f
1087,f
1035,f
1170,f
1064,f
1250,f
1129,f
1088,f
1037,f
1117,f
1095,f
1027,f
1027,f
1190,f
1153,f
1037,f
1120,f
1212,f
1024,f
1135,f
1177,f
1096,f
1114,f
1 Weight Sex
2 1607 m
3 1157 m
4 1248 m
5 1310 m
6 1398 m
7 1237 m
8 1232 m
9 1343 m
10 1380 m
11 1274 m
12 1245 m
13 1286 m
14 1508 m
15 1105 m
16 1123 m
17 1198 m
18 1300 m
19 1249 m
20 1185 m
21 915 m
22 1345 m
23 1107 m
24 1357 m
25 1227 m
26 1205 m
27 1435 m
28 1289 m
29 1093 m
30 1211 m
31 1260 m
32 1193 m
33 1330 m
34 1130 m
35 1357 m
36 1193 m
37 1232 m
38 1321 m
39 1260 m
40 1380 m
41 1230 m
42 1136 m
43 1029 m
44 1223 m
45 1240 m
46 1264 m
47 1020 m
48 1415 m
49 1410 m
50 1275 m
51 1230 m
52 1085 m
53 1048 m
54 1181 m
55 1103 m
56 1165 m
57 1547 m
58 1173 m
59 1660 m
60 1307 m
61 1535 m
62 1315 m
63 1257 m
64 1424 m
65 1309 m
66 1170 m
67 1412 m
68 1270 m
69 1230 m
70 1233 m
71 1561 m
72 1193 m
73 1272 m
74 1355 m
75 1137 m
76 1354 m
77 1110 m
78 1265 m
79 1407 m
80 1227 m
81 1330 m
82 1222 m
83 1305 m
84 1475 m
85 1177 m
86 1337 m
87 1145 m
88 1070 m
89 1305 m
90 1085 m
91 1303 m
92 1390 m
93 1532 m
94 1238 m
95 1233 m
96 1280 m
97 1245 m
98 1459 m
99 1157 m
100 1302 m
101 1385 m
102 1310 m
103 1342 m
104 1303 m
105 1248 m
106 1115 m
107 1365 m
108 1227 m
109 1353 m
110 1125 f
111 1027 f
112 1112 f
113 983 f
114 1090 f
115 1247 f
116 1045 f
117 983 f
118 972 f
119 1045 f
120 937 f
121 1245 f
122 1200 f
123 1270 f
124 1200 f
125 1145 f
126 1090 f
127 1040 f
128 1343 f
129 1010 f
130 1095 f
131 1180 f
132 1168 f
133 1095 f
134 1040 f
135 1235 f
136 1050 f
137 1038 f
138 1046 f
139 1255 f
140 1228 f
141 1000 f
142 1225 f
143 1220 f
144 1085 f
145 1067 f
146 1006 f
147 1138 f
148 1175 f
149 1252 f
150 1037 f
151 958 f
152 1020 f
153 1068 f
154 1107 f
155 1317 f
156 952 f
157 1056 f
158 1203 f
159 1183 f
160 1392 f
161 1130 f
162 1284 f
163 996 f
164 1228 f
165 1087 f
166 1035 f
167 1170 f
168 1064 f
169 1250 f
170 1129 f
171 1088 f
172 1037 f
173 1117 f
174 1095 f
175 1027 f
176 1027 f
177 1190 f
178 1153 f
179 1037 f
180 1120 f
181 1212 f
182 1024 f
183 1135 f
184 1177 f
185 1096 f
186 1114 f

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singtime
4.3
24.1
6.6
7.3
4
2.6
4
3.9
9.4
6.2
1.6
6.5
0.2
2.7
17.4
5.6
2
3.8
1.2
0.7
1.6
2.3
3.7
0.8
0.5
4.5
11.5
3.5
0.8
5.2
2
0.7
1.7
5
2.8
1.5
3.9
3.7
4.5
1.8
1.2
0.7
0.7
4.2
4.7
2.2
1.4
14.1
8.6
3.7
3.5
1 singtime
2 4.3
3 24.1
4 6.6
5 7.3
6 4
7 2.6
8 4
9 3.9
10 9.4
11 6.2
12 1.6
13 6.5
14 0.2
15 2.7
16 17.4
17 5.6
18 2
19 3.8
20 1.2
21 0.7
22 1.6
23 2.3
24 3.7
25 0.8
26 0.5
27 4.5
28 11.5
29 3.5
30 0.8
31 5.2
32 2
33 0.7
34 1.7
35 5
36 2.8
37 1.5
38 3.9
39 3.7
40 4.5
41 1.8
42 1.2
43 0.7
44 0.7
45 4.2
46 4.7
47 2.2
48 1.4
49 14.1
50 8.6
51 3.7
52 3.5

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Pulse
97
111
93
98
107
77
121
88
96
123
119
91
99
95
99
102
77
85
104
106
114
85
112
102
104
94
104
98
1 Pulse
2 97
3 111
4 93
5 98
6 107
7 77
8 121
9 88
10 96
11 123
12 119
13 91
14 99
15 95
16 99
17 102
18 77
19 85
20 104
21 106
22 114
23 85
24 112
25 102
26 104
27 94
28 104
29 98

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Branches
23
30
54
28
31
29
34
35
30
27
21
43
51
35
51
49
35
24
26
29
21
29
37
27
28
33
33
23
37
27
40
48
41
20
30
57
1 Branches
2 23
3 30
4 54
5 28
6 31
7 29
8 34
9 35
10 30
11 27
12 21
13 43
14 51
15 35
16 51
17 49
18 35
19 24
20 26
21 29
22 21
23 29
24 37
25 27
26 28
27 33
28 33
29 23
30 37
31 27
32 40
33 48
34 41
35 20
36 30
37 57

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Glucose
81
85
93
93
99
76
75
84
78
84
81
82
89
81
96
82
74
70
84
86
80
70
131
75
88
102
115
89
82
79
106
1 Glucose
2 81
3 85
4 93
5 93
6 99
7 76
8 75
9 84
10 78
11 84
12 81
13 82
14 89
15 81
16 96
17 82
18 74
19 70
20 84
21 86
22 80
23 70
24 131
25 75
26 88
27 102
28 115
29 89
30 82
31 79
32 106

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NerveCells
35
19
33
34
17
26
16
40
28
30
23
12
27
33
22
31
28
28
35
23
23
19
29
1 NerveCells
2 35
3 19
4 33
5 34
6 17
7 26
8 16
9 40
10 28
11 30
12 23
13 12
14 27
15 33
16 22
17 31
18 28
19 28
20 35
21 23
22 23
23 19
24 29

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RateChange,Treatment
28,Caffeine
11,Caffeine
-3,Caffeine
14,Caffeine
-2,Caffeine
-4,Caffeine
18,Caffeine
2,Caffeine
2,Caffeine
26,Decaf
1,Decaf
0,Decaf
-4,Decaf
-4,Decaf
14,Decaf
16,Decaf
8,Decaf
0,Decaf
18,Decaf
-10,Decaf
1 RateChange Treatment
2 28 Caffeine
3 11 Caffeine
4 -3 Caffeine
5 14 Caffeine
6 -2 Caffeine
7 -4 Caffeine
8 18 Caffeine
9 2 Caffeine
10 2 Caffeine
11 26 Decaf
12 1 Decaf
13 0 Decaf
14 -4 Decaf
15 -4 Decaf
16 14 Decaf
17 16 Decaf
18 8 Decaf
19 0 Decaf
20 18 Decaf
21 -10 Decaf

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NEConcentration,Treatment
543,Toluene
523,Toluene
431,Toluene
635,Toluene
564,Toluene
549,Toluene
535,Control
385,Control
502,Control
412,Control
387,Control
1 NEConcentration Treatment
2 543 Toluene
3 523 Toluene
4 431 Toluene
5 635 Toluene
6 564 Toluene
7 549 Toluene
8 535 Control
9 385 Control
10 502 Control
11 412 Control
12 387 Control

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Dopamine,Group
3420,toluene
2314,toluene
1911,toluene
2464,toluene
2781,toluene
2803,toluene
1820,control
1843,control
1397,control
1803,control
2539,control
1990,control
1 Dopamine Group
2 3420 toluene
3 2314 toluene
4 1911 toluene
5 2464 toluene
6 2781 toluene
7 2803 toluene
8 1820 control
9 1843 control
10 1397 control
11 1803 control
12 2539 control
13 1990 control

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Animal,Site I,Site II
1,50.6,38
2,39.2,18.6
3,35.2,23.2
4,17,19
5,11.2,6.6
6,14.2,16.4
7,24.2,14.4
8,37.4,37.6
9,35.2,24.4
1 Animal Site I Site II
2 1 50.6 38
3 2 39.2 18.6
4 3 35.2 23.2
5 4 17 19
6 5 11.2 6.6
7 6 14.2 16.4
8 7 24.2 14.4
9 8 37.4 37.6
10 9 35.2 24.4

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Subject,mCPP,Placebo
1,1.1,0
2,1.3,-0.3
3,1,0.6
4,1.7,0.3
5,1.4,-0.7
6,0.1,-0.2
7,0.5,0.6
8,1.6,0.9
9,-0.5,-2
1 Subject mCPP Placebo
2 1 1.1 0
3 2 1.3 -0.3
4 3 1 0.6
5 4 1.7 0.3
6 5 1.4 -0.7
7 6 0.1 -0.2
8 7 0.5 0.6
9 8 1.6 0.9
10 9 -0.5 -2

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Animal,Control,Regenerating
1,16.3,11.5
2,4.8,3.6
3,10.9,12.5
4,14.2,6.3
5,16.3,15.2
6,9.9,8.1
7,29.2,16.6
8,22.4,13.1
1 Animal Control Regenerating
2 1 16.3 11.5
3 2 4.8 3.6
4 3 10.9 12.5
5 4 14.2 6.3
6 5 16.3 15.2
7 6 9.9 8.1
8 7 29.2 16.6
9 8 22.4 13.1

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BodyTempDrop,AlcoholDose
0.2,1.5
1.9,1.5
-0.1,1.5
0.5,1.5
0.8,1.5
4,3
3.2,3
2.3,3
2.9,3
3.8,3
3.3,6
5.1,6
5.3,6
6.7,6
5.9,6
1 BodyTempDrop AlcoholDose
2 0.2 1.5
3 1.9 1.5
4 -0.1 1.5
5 0.5 1.5
6 0.8 1.5
7 4 3
8 3.2 3
9 2.3 3
10 2.9 3
11 3.8 3
12 3.3 6
13 5.1 6
14 5.3 6
15 6.7 6
16 5.9 6

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PeakFlow,Height
733,174
572,183
500,176
738,169
616,183
787,186
866,178
670,175
550,172
660,179
575,171
577,184
783,200
625,195
470,176
642,176
856,190
1 PeakFlow Height
2 733 174
3 572 183
4 500 176
5 738 169
6 616 183
7 787 186
8 866 178
9 670 175
10 550 172
11 660 179
12 575 171
13 577 184
14 783 200
15 625 195
16 470 176
17 642 176
18 856 190

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Patient,Before,After
1,98,75
2,100,60
3,82,25
4,100,55
5,93,78
6,119,102
7,70,58
8,78,70
9,104,90
10,70,50
11,60,65
12,88,45
13,45,36
14,159,144
15,65,27
16,98,90
17,66,16
18,67,53
1 Patient Before After
2 1 98 75
3 2 100 60
4 3 82 25
5 4 100 55
6 5 93 78
7 6 119 102
8 7 70 58
9 8 78 70
10 9 104 90
11 10 70 50
12 11 60 65
13 12 88 45
14 13 45 36
15 14 159 144
16 15 65 27
17 16 98 90
18 17 66 16
19 18 67 53

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LegStrength,UpperBodyStrength
55,low
70,low
45,low
246,low
240,low
96,low
225,low
40,middle
200,middle
250,middle
192,middle
117,middle
215,middle
181,high
85,high
416,high
228,high
257,high
316,high
134,high
1 LegStrength UpperBodyStrength
2 55 low
3 70 low
4 45 low
5 246 low
6 240 low
7 96 low
8 225 low
9 40 middle
10 200 middle
11 250 middle
12 192 middle
13 117 middle
14 215 middle
15 181 high
16 85 high
17 416 high
18 228 high
19 257 high
20 316 high
21 134 high

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function parameter = do_regression(x, y, start_parameter)
options = optimoptions('fminunc','GradObj','on');
fun = @exp_funct;
myfunc = @ (p)(lserr(p, x, y, fun));
parameter = fminunc(myfunc, start_parameter, options);

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../latex/environments.tex

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MAO and Schizophrenia Monoamine oxidase (MAO) is an enzyme that is
thought to play a role in the regulation of behavior. To see whether
different categories of schizophrenic patients have different levels
of MAO activity, researchers collected blood specimens from 42
patients and measured the MAO activity in the platelets. Values are
expressed as nmol benzylaldehyde product per 108 platelets per hour.

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Brain Weight: In 1888, P. Topinard published data on the brain weights
of hundreds of French men and women. Brain weights are given in
gram.

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Cricket Singing Times Male Mormon crickets (Anabrus simplex) sing to attract mates.
A field researcher measured the duration of 51 unsuccessful songs--that is, the time
until the singing male gave up and left his perch. The data is given
in minutes.

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Pulse after Exercise: A group of 28 adults did some moderate exercise
for five minutes and then measured their pulses. Data is given in
beats/minute.

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A dendritic tree is a branched structure that emanates from the body
of a nerve cell. As part of a study of brain development, 36 nerve
cells were taken from the brains of newborn guinea pigs. The
investigators counted the number of dendritic branch segments
emanating from each nerve cell.

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For each of 31 healthy dogs, a veterinarian measured the glucose
concentration in the anterior chamber of the right eye and also in the
blood serum. The following data are the anterior chamber glucose
measurements, expressed as a percentage of the blood glucose.

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A veterinary anatomist investigated the spatial arrangement of the
nerve cells in the intestine of a pony. He removed a block of tissue
from the intestinal wall, cut the block into many equal sections, and
counted the number of nerve cells in each of 23 randomly selected
sections.

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Researchers were interested in the short-term effect that caffeine has
on heart rate. They enlisted a group of volunteers and measured each
person's resting heart rate. Then they had each subject drink 6 ounces
of coffee. Nine of the subjects were given coffee containing caffeine
and 11 were given decaffeinated coffee. After 10 minutes each person's
heart rate was measured again. The data in the table contains the
change in heart rate; a positive number means that heart rate went up
and a negative number means that heart rate went down.

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Toluene and the Brain Abuse of substances containing toluene (for
example, glue) can produce various neurological symptoms. In an
investigation of the mechanism of these toxic effects, researchers
measured the concentrations of various chemicals in the brains of rats
that had been exposed to a toluene-laden atmosphere, and also in
unexposed control rats. The concentrations of the brain chemical
norepinephrine (NE) in the medulla region of the brain, for six
toluene-exposed rats and five control rats, are given in accompanying
data file in ng/g.

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In a pharmacological study, researchers measured the concentration of
the brain chemical dopamine in six rats exposed to toluene and six
control rats. Number are specified in ng/g.

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Nerve Cell Density For each of nine horses, a veterinary anatomist
measured the density of nerve cells at specified sites in the
intestine. The results for site I (midregion of jejunum) and site II
(mesenteric region of jejunum) are given in the accompanying dataset.
Each density value is the average of counts of nerve cells in five
equal sections of tissue.

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Hunger Rating During a weight loss study each of nine subjects was
given either the active drug m-chlorophenylpiperazine (mCPP) for two
weeks and then a placebo for another two weeks, or else was given the
placebo for the first two weeks and then mCPP for the second two
weeks. As part of the study the subjects were asked to rate how hungry
they were at the end of each two-week period.

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Certain types of nerve cells have the ability to regenerate a part of
the cell that has been amputated. In an early study of this process,
measurements were made on the nerves in the spinal cord in rhesus
monkeys. Nerves emanating from the left side of the cord were cut,
while nerves from the right side were kept intact. During the
regeneration process, the content of creatine phosphate (CP) was
measured in the left and the right portion of the spinal cord. The
following table shows the data for the right (control) side (Y1), and
for the left (regenerating) side (Y2). The units of measurement are mg
CP per 100 gm tissue.

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In an investigation of the physiological effects of alcohol
(ethanol), 15 mice were randomly allocated to three treatment groups,
each to receive a different oral dose of alcohol. The dosage levels
were 1.5, 3.0, and 6.0 g alcohol/kg body weight. The body temperature
of each mouse was measured immediately before the alcohol was given
and again 20 minutes afterward. The accompanying data shows the drop
(before minus after) in body temperature for each mouse. (The negative
value - 0.1 refers to a mouse whose temperature rose rather than
fell.)

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The peak flow rate of a person is the fastest rate
at which the person can expel air after taking a deep breath.
Peak flow rate is measured in units of liters per minute and
gives an indication of the person's respiratory health. Flow is given
in l/min, height in cm.

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An experiment was conducted to study the effect of tamoxifen on
patients with cervical cancer. One of the measurements made, both
before and again after tamoxifen was given, was microvessel density
(MVD). MVD, which is measured as number of vessels per mm$^2$, is a
measurement that relates to the formation of blood vessels that feed a
tumor and allow it to grow and spread.

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A group of female college students were divided into three groups
according to upper body strength. Their leg strength was tested by
measuring how many consecutive times they could leg press 246 pounds
before exhaustion. (The subjects were allowed only one second of rest
between consecutive lifts.)

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function y = exp_funct(A, tau, t)
y = A .* (1 - exp(-1 * (t./tau)));

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