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Project 1:
Juvenile Height
X value represents age, Y value represents average height in inches
ageheightdata = 881, 30<, 83, 36<, 85, 43<, 87, 48<, 89, 51<, 811, 56<, 813, 61<<881, 30<, 83, 36<, 85, 43<, 87, 48<, 89, 51<, 811, 56<, 813, 61<<
Plot1 = ListPlot@ageheightdataD
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lm = LinearModelFit@ageheightdata, x, xD
FittedModelB 28.8036 + 2.51786 x F
[email protected] + 2.51786 x
LM = Plot@lm@xD, 8x, 1, 13<, PlotStyle → GreenD
4 6 8 10 12
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Show@8Plot1, LM<D
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At birth according to the data the average neonate will be 28.8 inches. This is larger than the average
that is around 20 inches.
Using this data, at the of 27 an average human being would be ~96.79 inches or around 8 feet. This
could not possible be correct because humans peak their physical development during puberty.
US Carbon Dioxide Emissions
The X value represents the year and the Y value represents the annual carbon dioxide emission in
teragrams.
2 Project1.nb
data = 881991, 4697.7<, 81992, 4801.0<, 81993, 4921.9<, 81994, 4991.7<, 81995, 5040.6<,
81996, 5231.6<, 81997, 5296.9<, 81998, 5332.7<, 81999, 5399.6<, 82000, 5583.2<,
82001, 5518.8<, 82002, 5554.8<, 82003, 5615.4<, 82004, 5709.4<, 82005, 5748.7<<;
Plot2 = ListPlot@dataD
1992 1994 1996 1998 2000 2002 2004
4800
5000
5200
5400
5600
lm = LinearModelFit@data, x, xD
FittedModelB -142 897. + 74.1707 x F
Normal@lmD−142 897. + 74.1707 x
LM = Plot@lm@xD, 8x, 1991, 2005<, PlotStyle → GreenD
1994 1996 1998 2000 2002 2004
5000
5200
5400
5600
5800
Project1.nb 3
Show@8Plot2, LM<D
1992 1994 1996 1998 2000 2002 2004
4800
5000
5200
5400
5600
lm@"RSquared"D0.966382
In terms of RSquared the linear model is a pretty good fit to the data because it is close to 1. Visually
its an alright fit to the data.
The predicted estimated emissions according to the linear model do not accuratley display the actual
estimated carbon dioxide emission. The linear model may have broken down because of environmen-
tal laws that have been passed to reduce carbon dioxide emissions in the US.
Life Expectancy
The X value represents age and the Y value represents the life expectancy at the corresponding age.
4 Project1.nb
data = 880, 78.5<, 81, 78.0<, 85, 74.1<, 810, 69.1<,
815, 64.1<, 820, 59.3<, 825, 54.6<, 830, 49.8<, 835, 45.1<, 840, 40.4<,
845, 35.8<, 850, 31.3<, 855, 27.1<, 860, 23.0<, 865, 19.1<, 870, 15.5<,
875, 12.1<, 880, 9.1<, 885, 6.6<, 890, 4.7<, 895, 3.3<, 8100, 2.3<<;
Plot3 = ListPlot@dataD
20 40 60 80 100
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80
This is a plot of life expectancy versus age.
lm = LinearModelFit@data, x, xD
FittedModelB 75.2608 - 0.811454 x F
LM = Plot@lm@xD, 8x, 0, 100<, PlotStyle → GreenD
20 40 60 80 100
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60
Project1.nb 5
Show@8Plot3, LM<D
20 40 60 80 100
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lm@"RSquared"D0.984809
Visually and in terms of RSquared the linear model is a good fit. The Rsquared value is very close to 1
so it is a good fit.
At the age of 0, the life expectancy is 75.2. This suggests that the average human is expexted to live
75.2 years given a normal development. This doesn’t fit very well with the data because humans now a
days do live longer than 75 years seeing as the data has an expected life expectancy all the way up to
100 years old.
T = Table@8x, lm@xD<, 8x, 0, 100<D880, 75.2608<, 81, 74.4494<, 82, 73.6379<, 83, 72.8264<, 84, 72.015<, 85, 71.2035<,
86, 70.3921<, 87, 69.5806<, 88, 68.7692<, 89, 67.9577<, 810, 67.1463<,
811, 66.3348<, 812, 65.5234<, 813, 64.7119<, 814, 63.9005<, 815, 63.089<,
816, 62.2775<, 817, 61.4661<, 818, 60.6546<, 819, 59.8432<, 820, 59.0317<,
821, 58.2203<, 822, 57.4088<, 823, 56.5974<, 824, 55.7859<, 825, 54.9745<,
826, 54.163<, 827, 53.3516<, 828, 52.5401<, 829, 51.7287<, 830, 50.9172<,
831, 50.1057<, 832, 49.2943<, 833, 48.4828<, 834, 47.6714<, 835, 46.8599<,
836, 46.0485<, 837, 45.237<, 838, 44.4256<, 839, 43.6141<, 840, 42.8027<,
841, 41.9912<, 842, 41.1798<, 843, 40.3683<, 844, 39.5568<, 845, 38.7454<,
846, 37.9339<, 847, 37.1225<, 848, 36.311<, 849, 35.4996<, 850, 34.6881<,
851, 33.8767<, 852, 33.0652<, 853, 32.2538<, 854, 31.4423<, 855, 30.6309<,
856, 29.8194<, 857, 29.008<, 858, 28.1965<, 859, 27.385<, 860, 26.5736<,
861, 25.7621<, 862, 24.9507<, 863, 24.1392<, 864, 23.3278<, 865, 22.5163<,
866, 21.7049<, 867, 20.8934<, 868, 20.082<, 869, 19.2705<, 870, 18.4591<,
871, 17.6476<, 872, 16.8361<, 873, 16.0247<, 874, 15.2132<, 875, 14.4018<,
876, 13.5903<, 877, 12.7789<, 878, 11.9674<, 879, 11.156<, 880, 10.3445<,
881, 9.53306<, 882, 8.72161<, 883, 7.91016<, 884, 7.0987<, 885, 6.28725<,
886, 5.4758<, 887, 4.66434<, 888, 3.85289<, 889, 3.04144<, 890, 2.22998<,
891, 1.41853<, 892, 0.607075<, 893, −0.204379<, 894, −1.01583<, 895, −1.82729<,
896, −2.63874<, 897, −3.45019<, 898, −4.26165<, 899, −5.0731<, 8100, −5.88455<<
6 Project1.nb
Tabelofdata = ListPlot@8T<D
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Show@8Tabelofdata, Plot3<D
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High School Senior alcohol consumption
The X value represents the year of the survey and the Y value represents a proportion of high school
seniors who reported consuming alcohol in the past 30 dasys.
alcoholdata =
881980, 0.72<, 81990, 0.571<, 82000, 0.5009<, 82009, 0.435<, 82010, 0.412<<;
Project1.nb 7
Plot4 = ListPlot@alcoholdataD
1985 1990 1995 2000 2005 2010
0.45
0.50
0.55
0.60
0.65
0.70
lm = LinearModelFit@alcoholdata, x, xD
FittedModelB 19.5976 - 0.0095454 x F
LM = Plot@lm@xD, 8x, 1980, 2010<, PlotStyle → GreenD
1985 1990 1995 2000 2005 2010
0.45
0.50
0.55
0.60
0.65
0.70
Show@8Plot4, LM<D
1985 1990 1995 2000 2005 2010
0.45
0.50
0.55
0.60
0.65
0.70
8 Project1.nb
lm@"RSquared"D0.972251
Visually and in terms of RSquared the linear model is a good fit for the data because it is very close to 1.
T = Table@8x, lm@xD<, 8x, 1980, 2010<D881980, 0.697688<, 81981, 0.688143<, 81982, 0.678597<,
81983, 0.669052<, 81984, 0.659507<, 81985, 0.649961<, 81986, 0.640416<,
81987, 0.63087<, 81988, 0.621325<, 81989, 0.61178<, 81990, 0.602234<,
81991, 0.592689<, 81992, 0.583143<, 81993, 0.573598<, 81994, 0.564053<,
81995, 0.554507<, 81996, 0.544962<, 81997, 0.535416<, 81998, 0.525871<,
81999, 0.516326<, 82000, 0.50678<, 82001, 0.497235<, 82002, 0.487689<,
82003, 0.478144<, 82004, 0.468599<, 82005, 0.459053<, 82006, 0.449508<,
82007, 0.439962<, 82008, 0.430417<, 82009, 0.420871<, 82010, 0.411326<<
TableForm@T, TableHeadings → 8None, 8"Year", "% Seniors"<<DYear % Seniors
1980 0.697688
1981 0.688143
1982 0.678597
1983 0.669052
1984 0.659507
1985 0.649961
1986 0.640416
1987 0.63087
1988 0.621325
1989 0.61178
1990 0.602234
1991 0.592689
1992 0.583143
1993 0.573598
1994 0.564053
1995 0.554507
1996 0.544962
1997 0.535416
1998 0.525871
1999 0.516326
2000 0.50678
2001 0.497235
2002 0.487689
2003 0.478144
2004 0.468599
2005 0.459053
2006 0.449508
2007 0.439962
2008 0.430417
2009 0.420871
2010 0.411326
Project1.nb 9
Plot5 = ListPlot@TD
1985 1990 1995 2000 2005 2010
0.45
0.50
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0.65
0.70
Solve@lm@xD == 0, xD88x → 2053.09<<
I don’t think seems reasonable because I think high school students will always be rebellious and
choose to drink.
Solve@lm@xD � 1, xD88x → 1948.33<<
I don’t think this seems reasonable as well because I think high school students back then still drank
alcohol.
10 Project1.nb
World population estimates
populationdata = 881950, 2 525 779 000<,
81951, 2 572 851 000<, 81952, 2 619 292 000<, 81953, 2 665 865 000<,
81954, 2 713 172 000<, 81955, 2 761 651 000<, 81956, 2 811 572 000<,
81957, 2 863 043 000<, 81958, 2 916 030 000<, 81959, 2 970 396 000<,
81960, 3 026 003 000<, 81961, 3 082 830 000<, 81962, 3 141 072 000<,
81963, 3 201 178 000<, 81964, 3 263 739 000<, 81965, 3 329 122 000<,
81966, 3 397 475 000<, 81967, 3 468 522 000<, 81968, 3 541 675 000<,
81969, 3 616 109 000<, 81970, 3 691 173 000<, 81971, 3 766 754 000<,
81972, 3 842 874 000<, 81973, 3 919 182 000<, 81974, 3 995 305 000<,
81975, 4 071 020 000<, 81976, 4 146 136 000<, 81977, 4 220 817 000<,
81978, 4 295 665 000<, 81979, 4 371 528 000<, 81980, 4 449 049 000<,
81981, 4 528 235 000<, 81982, 4 608 962 000<, 81983, 4 691 560 000<,
81984, 4 776 393 000<, 81985, 4 863 602 000<, 81986, 4 953 377 000<,
81987, 5 045 316 000<, 81988, 5 138 215 000<, 81989, 5 230 452 000<,
81990, 5 320 817 000<, 81991, 5 408 909 000<, 81992, 5 494 900 000<,
81993, 5 578 865 000<, 81994, 5 661 086 000<, 81995, 5 741 822 000<,
81996, 5 821 017 000<, 81997, 5 898 688 000<, 81998, 5 975 304 000<,
81999, 6 051 478 000<, 82000, 6 127 700 000<, 82001, 6 204 147 000<,
82002, 6 280 854 000<, 82003, 6 357 992 000<, 82004, 6 435 706 000<,
82005, 6 514 095 000<, 82006, 6 593 228 000<, 82007, 6 673 106 000<,
82008, 6 753 649 000<, 82009, 6 834 722 000<, 82010, 6 916 183 000<<;
Plot6 = ListPlot@populationdataD
1960 1970 1980 1990 2000 2010
3 µ 109
4 µ 109
5 µ 109
6 µ 109
7 µ 109
lm = LinearModelFit@populationdata, x, xD
FittedModelB -1.46235µ1011
+ 7.61555µ107
x F
Project1.nb 11
LM = Plot@lm@xD, 8x, 1950, 2010<, PlotStyle → GreenD
1960 1970 1980 1990 2000 2010
3 µ 109
4 µ 109
5 µ 109
6 µ 109
Show@8LM, Plot6<D
1960 1970 1980 1990 2000 2010
3 µ 109
4 µ 109
5 µ 109
6 µ 109
lm@"RSquared"D0.995437
Visually and in terms of RSquared the linear model fits very well with the data. The linear model sug-
gests that the estimated annual rate of increase of world population is 76,155,000.
Solve@lm@xD � 9 000 000 000, xD88x → 2038.39<<
The linear model suggest the world will reach 9 billion people sometime in the year of 2038. I don’t
think this is reasonable because as a planet today we can barely sustain our resources with our current
population. I believe that in the future we may experience population control like in China.
Solve@lm@xD � 0, xD88x → 1920.21<<
The linear model suggests that in 1920 the world population was 0. This is definitley not reasonable as
humans have been occupying this planet for about 200,000 years.
Rates of Diabetes, US States:1994-2010
12 Project1.nb
Rates of Diabetes, US States:1994-2010
TXdata = 881994, 5.2<, 81995, 4.7<, 81996, 5<, 81997, 5.1<, 81998, 5.9<,
81999, 6<, 82000, 6.5<, 82001, 6.8<, 82002, 7.4<, 82003, 7.6<, 82004, 7.9<,
82005, 7.8<, 82006, 8.8<, 82007, 9.3<, 82008, 9.8<, 82009, 9.6<, 82010, 9.5<<881994, 5.2<, 81995, 4.7<, 81996, 5<, 81997, 5.1<, 81998, 5.9<,
81999, 6<, 82000, 6.5<, 82001, 6.8<, 82002, 7.4<, 82003, 7.6<, 82004, 7.9<,
82005, 7.8<, 82006, 8.8<, 82007, 9.3<, 82008, 9.8<, 82009, 9.6<, 82010, 9.5<<
ListPlot@TXdataD
1995 2000 2005 2010
5
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lm = LinearModelFit@TXdata, x, xD
FittedModelB -675.315 + 0.340931 x F
lm@1999D
6.206617647058806`
Project1.nb 13
The linear fumction for TX’s data gives calculations that are slight off from the collected data. This also
happens with CA’s linear model and actual collected data.
14 Project1.nb