Elevation of Missouri Farmland

Inputting and graphing the data

>    x:=[0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1,1.1,1.2,1.3,1.4,1.5]:
y:=[0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1,1.1,1.2,1.3,1.4,1.5]:
r[16]:=[800.3,799.1,798.3,797.8,797.5,797.4,797.4,797.5,797.6,797.7,797.6,797.3,796.8,796.0,794.8,793.2]:
r[15]:=[800.8,799.6,798.8,798.3,798.0,797.9,797.9,798.0,798.1,798.1,798.1,797.8,797.3,796.5,795.3,793.7]:
r[14]:=[801.2,800.0,799.2,798.7,798.4,798.3,798.3,798.4,798.5,798.6,798.5,798.2,797.7,796.9,795.7,794.1]:
r[13]:=[801.6,800.4,799.6,799.1,798.8,798.7,798.7,798.8,798.9,798.9,798.9,798.6,798.1,797.3,796.1,794.5]:
r[12]:=[801.9,800.7,799.9,799.4,799.1,799.0,799.0,799.1,799.2,799.3,799.2,798.9,798.4,797.6,796.4,794.8]:
r[11]:=[802.2,801.0,800.2,799.7,799.4,799.3,799.3,799.4,799.5,799.5,799.5,799.2,798.7,797.9,796.7,795.1]:
r[10]:=[802.4,801.2,800.4,799.9,799.6,799.5,799.5,799.6,799.7,799.8,799.7,799.4,798.9,798.1,796.9,795.3]:
r[9]:=[802.6,801.4,800.6,800.1,799.8,799.7,799.7,799.8,799.9,799.9,799.9,799.6,799.1,798.3,797.1,795.5]:
r[8]:=[802.7,801.5,800.7,800.2,799.9,799.8,799.8,799.9,800.0,800.1,800.0,799.7,799.2,798.4,797.2,795.6]:
r[7]:=[802.8,801.6,800.8,800.3,800.0,799.9,799.9,800.0,800.1,800.1,800.1,799.8,799.3,798.5,797.3,795.7]:
r[6]:=[802.8,801.6,800.8,800.3,800.0,799.9,799.9,800.0,800.1,800.2,800.1,799.8,799.3,798.5,797.3,795.7]:
r[5]:=[802.8,801.6,800.8,800.3,800.0,799.9,799.9,800.0,800.1,800.1,800.1,799.8,799.3,798.5,797.3,795.7]:
r[4]:=[802.7,801.5,800.7,800.2,799.9,799.8,799.8,799.9,800.0,800.1,800.0,799.7,799.2,798.4,797.2,795.6]:
r[3]:=[802.6,801.4,800.6,800.1,799.8,799.7,799.7,799.8,799.9,799.9,799.9,799.6,799.1,798.3,797.1,795.5]:
r[2]:=[802.4,801.2,800.4,799.9,799.6,799.5,799.5,799.6,799.7,799.8,799.7,799.4,798.9,798.1,796.9,795.3]:
r[1]:=[802.2,801.0,800.2,799.7,799.4,799.3,799.3,799.4,799.5,799.5,799.5,799.2,798.7,797.9,796.7,795.1]:

Pointplot of data:

[Maple Plot]

formula for elevation - and the graph

The formula below (and its graph) uses "x and y" instead of "e and n":

surf2 := z = -10.15370723*x^3+21.39713679*x^2-2.500000000*y^2-13.98386804*x+2.497794118*y+802.1982359

[Maple Plot]

Using "e and n", and rounding coefficients to three decimal places we have the formula:

E = -10.154*e^3+21.397*e^2-2.5*n^2-13.984*e+2.498*n+802.198 .

cross sectional model (from data)

(elevation 0.6 miles north of southern fence)

[Maple Plot]

Highlighting the elevations along the line "n=0.6" (a cross-section)

[Maple Plot]

Using the TI-83 we find that when n=0.6, the elevation E is given as a function of e:

E = -10.124*e^3+21.347*e^2-13.972*e+802.809 .

Drawing this "cross sectional model" into our picture of the data we get:

[Maple Plot]

cross sectional model (from elevation formula)

We saw earlier that the Elevation of Missouri Farmland Data is pretty well approximated by the formula

E = -10.15370723*e^3+21.39713679*e^2-2.500000000*n^2-13.98386804*e+2.497794118*n+802.1982359 .

If we fix n as 0.6, this gives us (upon rounding)

E = -10.154*e^3+21.397*e^2-.900-13.984*e+1.499+802.198 , which is E = -10.154*e^3+21.397*e^2-13.984*e+802.797 .

[Maple Plot]

Compare this to our cross sectional model found from the data: E = -10.124*e^3+21.347*e^2-13.972*e+802.809 .

Very similar!