Predicting water quality for an area of 40 km2. Refer to given Exercise.
(a) Find a 95% confidence interval for mean response corresponding to an area of 40 km2.
(b) Find a 95% prediction interval for a future response corresponding to an area of 40 km2.
(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 other states? Explain why or why not.
Exercises
Predicting water quality. The index of biotic integrity (IBI) is a measure of the water quality of 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.9 Table 10.4 gives the data for IBI, the percent of the watershed area that was forest, and the area of the watershed in square kilometers for streams in the original sample with area less than or equal to 70 square kilometers.
(a) Use numerical and graphical methods to describe the variable IBI. Do the same for area. Summarize your results.
(b) Plot the data for IBI and area 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 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 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.
