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The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use m

Question: The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use measures for a collection of streams in the Ozark Highland eco-region of Arkansas were collected as part of a study. Table 10.2 gives the data for IBI and the area of the watershed in square kilometers for streams in the original sample with area less than or equal to 70 km².

TABLE 10.2

Watershed area and index of biotic integrity

Area IBI	Area IBI	Area IBI	Area IBI	Area IBI
21 47 34 76 6 33 47 78 10 62 49 78 23 33 32 64 12 83 16 67	29 61 49 85 28 46 8 53 57 55 9 71 31 59 10 41 21 82 26 56	31 39 52 89 21 32 8 43 18 29 5 55 18 81 26 82 27 82 26 85	32 59 2 74 59 80 58 88 19 29 14 58 16 71 9 60 23 86 28 91	34 72 70 89 69 80 54 84 39 54 9 71 21 75 54 84 26 79

a). Use numerical and graphical methods to describe the variable IBI. Do the same for area. Summarize your results.

b). Plot the data and describe the relationship. Are there any outliers or unusual patterns?

c). Give the statistical model for simple linear regression for this problem.

d). State the null and alternative hypothesis for examining the relationship between IBI and area.

e). Run the simple linear regression and summarize the results.

f). Obtain the residuals and plot them versus area. Is there anything unusual in the plot?

g). Do the residuals appear to be approximately Normal? Give reasons for your answer.

h). Do the assumptions for the analysis of these data using the model you gave in part c) appear to be reasonable? Explain your answer.

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The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use m

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