Homework 10 and 11

Spatial Analysis, Spring 2000

Due Apr. 28 2000

Correlation (10 points)

1. You are given the following map of six hot spring districts in Idaho. You are also given the following table that lists the temperature of the water in the springs:

   

   Spring	X	Y	temp.
   1	11	30	16
   2	15	31	31
   3	18	24	40
   4	19	20	38
   5	15	15	29
   6	23	11	44
   7	28	14	50
   8	35	12	51
   9	29	15	60
   10	27	32	55
   11	27	28	54
   12	36	31	67
   13	42	28	88
   14	40	22	79
   15	32	28	69
   16	38	20	88
   17	46	18	90
   18	48	12	97

   The areas of the regions (in square miles) are as follows:

   
   

   region	area
   A	42
   B	21
   C	11
   D	19
   E	22
   F	9

   Use a $\chi^2$ test to find if the number of points are evenly distributed across the regions, given their areas. As always, state your hypothesis, show your calculations, and state your conclusion.

   
   

   It has been suggested that there is a difference in the temperature of the springs in the different regions. Thest this hypothesis using a $\chi^2$ analysis. Note: remember that a $\chi^2$ analysis requires that there be at least 5 observations per category. In this case, you will have to group some of the regions together so that they have a combined number of 5 or more observations.

Autocorrelation (10 points)

It has been suggested if the springs were emenating from a central source, that there would be a significant level of autocorrelation between districts.

1. State your hypothesis for testing autocorrelation between the six districts:
   
   
   
   
   
   
   
   
2. Show your calculation for Moran's I to test your hypotheses.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
3. Show your test statistic. What is your conclusion regarding your hypothesis?

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Homework 10 and 11

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