> A := [seq(1790+10*k,k=0..20)];
A := [ 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 , , , , , , , , , , , , , , 1930 1940 1950 1960 1970 1980 1990 , , , , , , ]
> N := [3.9, 5.3, 7.2, 9.6, 12.9, 17.1, 23.2, 31.4, 38.6, 50.2, 62.9, 76.0, 92.0, 105.7, 122.8, 131.7, 150.7, 179.3, 203.3, 226.5, 248.7];
N := [ 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 38.6 50.2 62.9 76.0 92.0 105.7 122.8 131.7 , , , , , , , , , , , , , , , , 150.7 179.3 203.3 226.5 248.7 , , , , ]
> with(plots):
Warning, the name changecoords has been redefined
> lnN := map(ln,N);
lnN := [ 1.360976553 1.667706821 1.974081026 2.261763098 2.557227311 2.839078464 , , , , , , 3.144152279 3.446807893 3.653252276 3.916015027 4.141546164 4.330733340 , , , , , , 4.521788577 4.660604893 4.810557016 4.880526609 5.015291106 5.189060381 , , , , , , 5.314682721 5.422744945 5.516247351 , , ]
Error, unable to execute seq
> with(linalg):
Warning, the protected names norm and trace have been redefined and unprotected
> punkte := plot([seq([A[j],lnN[j]],j=1..vectdim(A))],style=point, title="US-Bevoelkerung", labels=["Jahr","ln(Einwohner)"]);
punkte := PLOT CURVES [ ( ( [ 1790. 1.36097655299999997 [ , ] , 1800. 1.66770682099999988 , ] , [ 1810. 1.97408102599999991 [ , ] , 1820. 2.26176309799999986 , ] ,
[ 1830. 2.55722731100000011 [ , ] , 1840. 2.83907846399999996 , ] , [ 1850. 3.14415227900000005 [ , ] , 1860. 3.44680789299999990 , ] , [ 1870. 3.65325227599999991 [ , ] , 1880. 3.91601502699999981 , ] , [ 1890. 4.14154616400000020 [ , ] , 1900. 4.33073334000000010 , ] , [ 1910. 4.52178857699999970 [ , ] , 1920. 4.66060489300000036 , ] , [ 1930. 4.81055701599999974 [ , ] , 1940. 4.88052660900000034 , ] , [ 1950. 5.01529110600000028 [ , ] , 1960. 5.18906038099999999 , ] , [ 1970. 5.31468272099999961 [ , ] , 1980. 5.42274494499999982 , ] ,
[ 1990. 5.51624735099999963 ] , ] , COLOUR ( RGB 1.0 0. 0. , , , ) ) , STYLE POINT ( ) ,
( )
TITLE "US-Bevoelkerung" , AXESLABELS ( "Jahr" "ln(Einwohner)" , ) ,
( )
VIEW DEFAULT DEFAULT ) ,
Error, unable to execute seq
> display(punkte);
US-Bevoelkerung
2 3 4 5
ln(Einwohner)
1800 1850 1900 1950
Jahr
> # bis 1890 und ab 1900, weshalb ein knick?
> A_a := [seq(A[k],k=1..11)];
:=
A_a [ 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 , , , , , , , , , , ]
> lnN_a := [seq(lnN[k],k=1..11)];
lnN_a := [ 1.360976553 1.667706821 1.974081026 2.261763098 2.557227311 , , , , ,
2.839078464 3.144152279 3.446807893 3.653252276 3.916015027 4.141546164 , , , , , ]
> A_e := [seq(A[k],k=11..vectdim(A))];
:=
A_e [ 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 , , , , , , , , , , ]
> lnN_e := [seq(lnN[k],k=11..vectdim(A))];
lnN_e := [ 4.141546164 4.330733340 4.521788577 4.660604893 4.810557016 4.880526609 , , , , , , 5.015291106 5.189060381 5.314682721 5.422744945 5.516247351 , , , , ]
> read quadapprox:
Warning, ‘n‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘mittel‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘sigxy‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘sigx2‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘sigy2‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘m‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘q‘ is implicitly declared local to procedure ‘quadapprox‘
Warning, ‘c‘ is implicitly declared local to procedure ‘quadapprox‘
> G_a := quadapprox(A_a,lnN_a);
"[q, m, c]"
:=
G_a [ -48.85678387 .02808237300 .9989618633 , , ]
> G_e := quadapprox(A_e,lnN_e);
"[q, m, c]"
:=
G_e [ -21.35496625 .01352897900 .9961298832 , , ]
> gerade_a := plot(G_a[1]+G_a[2]*x,x=1790..1890,style=line);
gerade_a := PLOT CURVES [ ( ( [ 1790. 1.41066380000000180 , , ] [ 1792.17971541666656 1.47187538136468277 , , ]
[ 1794.07627414583340 1.52513525101355185 , , ]
[ 1796.20915279166662 1.58503154470957241 , , ]
[ 1798.35616954166676 1.64532486992032289 , , ]
[ 1800.49298189583328 1.70533163148103739 , , ]
[ 1802.47408047916656 1.76096558084797294 , , ]
[ 1804.52539331250000 1.81857131297333296 , , ]
[ 1806.64686397916671 1.87814724354322492 , , ]
[ 1808.76153106249990 1.93753211334821174 , , ]
[ 1810.93672608333327 1.99861675127099402 , , ]
[ 1812.85263904166664 2.05242013360244612 , , ]
[ 1815.00950325000008 2.11298999881121574 , , ]
[ 1817.17522374999999 2.17380856970596169 , , ]
[ 1819.26229674999990 2.23241853217018616 , , ]
[ 1821.15755897916665 2.28564199302245896 , , ]
[ 1823.41120908333324 2.34892983585915260 , , ]
[ 1825.32034633333342 2.40254294022184922 , , ]
[ 1827.54112681249990 2.46490772598892249 , , ]
[ 1829.50689383333338 2.52011112869907094 , , ]
[ 1831.66365181250012 2.58067801074075475 , , ]
[ 1833.71739543750004 2.63835200526437319 , , ]
[ 1835.86026145833330 2.69852876815043884 , , ]
[ 1837.82808139583335 2.75378982163215369 , , ]
[ 1839.95064104166658 2.81339633332118666 , , ]
[ 1842.15538397916657 2.87531074686118159 , , ]
[ 1844.07461918750005 2.92920742585633320 , , ]
[ 1846.14744579166677 2.98741731571886504 , , ]
[ 1848.28887850000001 3.04755382778868266 , , ]
[ 1850.38385262499992 3.10638567259227472 , , ]
[ 1852.41084781249992 3.16330850751685943 , , ]
[ 1854.66148037499988 3.22651161062292857 , , ]
[ 1856.68377383333336 3.28330240983530785 , , ]
[ 1858.84300374999998 3.34393870974789564 , , ]
[ 1860.79958697916663 3.39888420979490034 , , ]
[ 1862.93864925000003 3.45895415435467157 , , ]
[ 1864.95134014583323 3.51547529082516519 , , ] [ 1867.05518206250008 3.57455616426203448 , , ] [ 1869.11207208333326 3.63231851704705378 , , ] [ 1871.26544531250011 3.69279034727672694 , , ] [ 1873.33939966666662 3.75103190703541145 , , ] [ 1875.46031754166665 3.81059231390352693 , , ] [ 1877.56367314583326 3.86965953053137212 , , ] [ 1879.49643850000007 3.92393616812856294 , , ] [ 1881.71160570833331 3.98614331993034909 , , ] [ 1883.69287766666662 4.04178213807870179 , , ] [ 1885.80532681249997 4.10110472293552419 , , ]
[ 1887.82721018749999 4.15788400603477726 [ , ] , 1890. 4.21890110000000362 , ] ],
( )
COLOUR RGB 1.0 0. 0. ) , , , , STYLE LINE ( ) , AXESLABELS ( "x" "" , ) ,
( )
VIEW 1790. .. 1890. DEFAULT ) ,
> gerade_e := plot(G_e[1]+G_e[2]*x,x=1890..2000,style=line);
gerade_e := PLOT CURVES [ ( ( [ 1890. 4.21480405999999874 , , ] [ 1892.39768695833322 4.24724231650786521 , , ]
[ 1894.48390156041660 4.27546667004894232 , , ]
[ 1896.83006807083324 4.30720790749887428 , , ]
[ 1899.19178649583342 4.33915954647461176 , , ]
[ 1901.54228008541668 4.37095932488772120 , , ]
[ 1903.72148852708324 4.40044179013164793 , , ]
[ 1905.97793264374991 4.43096917520070832 , , ]
[ 1908.31155037708322 4.46254064050900112 , , ]
[ 1910.63768416874996 4.49401085572765168 , , ]
[ 1913.03039869166673 4.52638184026118750 , , ]
[ 1915.13790294583328 4.55489422105821617 , , ]
[ 1917.51045357499993 4.58699240869664848 , , ]
[ 1919.89274612500003 4.61922239457745576 , , ]
[ 1922.18852642499996 4.65028195804476851 , , ]
[ 1924.27331487708330 4.67848701723244885 , , ]
[ 1926.75232999166656 4.71202556065832567 , , ]
[ 1928.85238096666672 4.74043710619803349 , , ]
[ 1931.29523949374993 4.77348648791091179 , , ]
[ 1933.45758321666676 4.80274079072903604 , , ]
[ 1935.83001699374995 4.83483739747808627 , , ]
[ 1938.08913498125002 4.86540095728949495 , , ]
[ 1940.44628760416663 4.89729082562472938 , , ]
[ 1942.61088953541662 4.92657567969597210 , , ]
[ 1944.94570514583324 4.95816335105816818 , , ] [ 1947.37092237708339 4.99097406405019228 , , ] [ 1949.48208110625001 5.01953588616275326 , , ] [ 1951.76219037083342 5.05038343652100607 , , ] [ 1954.11776635000001 5.08225197447605481 , , ] [ 1956.42223788749993 5.11342912151298989 , , ] [ 1958.65193259374996 5.14359461437025800 , , ] [ 1961.12762841249992 5.17708825111251513 , , ] [ 1963.35215121666670 5.20718377341510674 , , ] [ 1965.72730412500005 5.23931716723373952 , , ] [ 1967.87954567708334 5.26843479799480008 , , ] [ 1970.23251417500001 5.30026805939077761 , , ] [ 1972.44647416041676 5.33022067754032136 , , ] [ 1974.76070026875004 5.36152979396121409 , , ] [ 1977.02327929166677 5.39214017804809486 , , ] [ 1979.39198984375003 5.42418641336430696 , , ] [ 1981.67333963333340 5.45505074675923395 , , ] [ 1984.00634929583339 5.48661398548999557 , , ] [ 1986.32004046041675 5.51791586466812944 , , ] [ 1988.44608235000010 5.54667904074542050 , , ] [ 1990.88276627916662 5.57964488645275125 , , ] [ 1993.06216543333334 5.60912993184209085 , , ] [ 1995.38585949375010 5.64056713998789405 , , ]
[ 1997.60993120624994 5.67065655948080049 [ , ] , 2000. 5.70299174999999892 , ] ],
( )
COLOUR RGB 1.0 0. 0. ) , , , , STYLE LINE ( ) , AXESLABELS ( "x" "" , ) ,
( )
VIEW 1890. .. 2000. DEFAULT ) ,
> display(punkte,gerade_a,gerade_e);
US-Bevoelkerung
2 3 4 5
ln(Einwohner)
1800 1850 1900 1950 2000
Jahr