Homework Assignment 2

AWER 5930/6930

Spring 2003

1.

It has been proposed that there is a relationship between soil type and water depth in the shallow waters of the Loxahatchee inlet, in southeast Florida. In lab you calculated a contingency table and used the $\chi^2$ statistic to investigate the correlation.

(a)

Show the contingency tables and chi-square calculations that you did in lab.

(b)

What are your spatial units?

(c)

What do your expected values signify?

(d)

If your observed and expected values were very similar, what would that say about a correlation between soil type and depth? What kind of $\chi^2$ value would that produce?

(e)

What $\chi^2$ statistic did you obtain?

(f)

Is there a correlation between soil type and water depth?

2.

Recalculate your contengency tables, but using square meters as your spatial unit.

(a)

What $\chi^2$ statistic do you calculate?

(b)

Is there a correlation between soil type and depth?

3.

You are given the GPS locations of several magenetic anomoly readings in an area of southern Nevada. It has been suggested that the values of the readings are somehow affected by the underlying geology of the area. When you compare the values of the readings to the underlying geology, do you find a significant difference between aggregate values of readings and type of underlying deposit? State your null hypothesis, assumptions, and show all intermediate calculations.

4.

In lab you calculated a correlation coefficient between reading level and distance to a particular mining road. Now, you are asked to calculate a regression coefficient for the same data set, to see if the magenetic level is a function of distance from the mining road.

(a)

What regression equation do you obtain?

(b)

What r² value to you obtain?

(c)

How different are the results of this regression from your correlation calculations in lab?

(d)

Are the readings related to distance from the road?