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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 ecoregion of Arkansas were collected as part of a study.
10.32 Use the data set IBI.xlsx; complete all parts of the problem, use software only for parts(a), (b), (e), and (f).
a) Use numerical and graphical methods to describe the variable IBI. Do the same for area. Summarize your result.
b) Plot the data and describe the relationship between IBI and area. 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 hypotheses 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 are. Is there anything unusual in the plot?
g) Do the residuals appear to be approximately Normal? Give reasons for your answers.
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.
10.36 use the regression output from 10.32 to do the calculations for this problem by hand. You will have to calculate SSxx(easily done in Excel) to get your SE's.
a) Find a 95% confidence interval for the mean response corresponding to an area of 40(sqKm)
b) Find a 95% confidence interval for a future response corresponding to an area of 40(sqKm)
c) Write a short paragraph interpreting the meaning of the intervals in terms of Ozark Highland streams.
d) Do you think that these results can be applied to other streams in Arkansas or in our states? Explain why or why not.
