Department of Mathematics Education

J. Wilson, EMAT 6680

 


 

EMAT 6680 Assignment #12:
Spreadsheet in Mathematics

 

Matthew Tanner

EMAT 6680

Write-up #12

July 26, 2004

 

 

 

 

This data is from the lumber industry, giving the approximate number of board feet of lumber per tree in a forest of a given age. What function will fit the data? Predict the harvest for ages other than those given.

 

The graph of the Tree Data depicts what the data indicates and as you might otherwise expect that the yield in board feet of harvested timber increases with the age of the tree.

 

 

Simple linear regression produces a model equation that approximates the data. The method of least squares seeks to minimize the error between the values predicted by the model and the observed values.

 

 

The slope of the least squares equation is given by:

 

.

 

The y-intercept is given by:

 

.

 

 

Simple linear regression approximates the observed data in only a general way

 

 

Curve fitting functions in Excel and numerical programming applications will interpolate polynomial functions to the observed data. In the case of the tree data, the available observations suggest an polynomial function of degree two,

 

 

 

Dedicated numerical programming software such as Maple will interpolate a function to any required precision.

 

> with(CurveFitting):

PolynomialInterpolation([[20,1],[40,6],[80,33],[100,56],[12

120,88],[160,182],[200,320]], z);