GEOG 2043 ENVIRONMENTAL FIELD TECHNIQUES LAB 10 ASSESSING THE STRENGTH OF A STRAIGHT-LINE RELATION

OBJECTIVES:

• To calculate the parameters (slope and intercept) of a straight line using data from separate field studies.

• To evaluate the statistical significance of the computed relations.

• To understand the use of linear regression as a statistical method.

BACKGROUND: One of the data sets for this lab come from a project evaluating the history of fire in forests of the Colorado Front Range.  The topic of fire history and fire suppression has become an interesting issue in forest management circles.  Dr. Thomas Veblen and his graduate students are studying cycles of fire in many different types of forests; they hope to reconstruct paleo-fire regimes so that future management may attempt to reflect natural historic systems.  The data from this project include measurements of tree diameter at breast height (DBH) versus age.  The ages are determined by counting the number of tree rings in a sample obtained with an increment borer.  Given sufficient data, a general relation between age and DBH might be established, and that relation might then be used to determine ages of trees simple from measurements of DBH.   The technique hinges, in part, on the strength of the regression relation.

The second set of data come from a study of the channel characteristics of the Colorado River in areas near Grand Junction.  These areas provide important habitat for the Colorado Pikeminnow, one of four endangered fish in the upper Colorado River basin.  Dr. John Pitlick and his students have been studying this area to understand why the endangered fish prefer certain habitats over others.  As part of this work they have systematically measured downstream changes in channel characteristics, including the streambed sediment and the bankfull width and depth.  The data will be used to test a hypothesis about the downstream change in bankfull width.
 

TASKS: We will provide you with two separate spreadsheets, one containing the tree data and the other containing the river data.  For each data set we want you to calculate the values of the regression coefficients, b and m, and to perform a t-test to evaluate the significance of the relation.

1. The regression coefficients are calculated from the following equations:
 

a) To estimate these values you first need to calculate the mean of X and the mean of Y.

b) You then need to make additional columns to calculate individual values of  X i- X, Yi - Y, the product of these two, and values of (Xi -X)^2.

c) Sum the values in the column listing the product, and sum the values listing the squares, and use the formula above to compute m.

d) using that value and the means of X and Y, calculate b.

2. The hypothesis of zero slope (no significant relation between x and y) is stated as follows:

Ho: m = 0

H1: m * 0

where sem is the standard error of the regression coefficient m.  The function LINEST returns the value of sem.
 

Turn In:

1. Plots of each data set

2. A table summarizing the results of your statistical tests

3. One paragraph commenting on the results for each data set.