1. Pollution of water resources is a serious problem that can require substantial efforts and funds to rectify. In order to determine the nancial resources required, an accurate assessment of the water quality, which is measured by the index of biotic integrity (IBI), is needed. Since lBI is very expensive to measure, a study was done for a collection of streams in the Ozark Highland ecoregion of Arkansas in which the TB] for each stream was measured along with land use measures that are inexpensive to obtain. The land use measures collected in the study are the area of the watershed in square kilometers, Area, and the percent of the watershed area that is forest, Forest. The objective of this study is to determine if these land use measures can predict the lBI so that the funding required for pollution clean up can be accurately estimated. The data collected from the n = 49 watersheds are provided in the le ozcrknsu. A. Create a scatterplots to show the relationship between IBI and each of the explanatory variables. B. Using the plots created in part A., does each explanatory variable seem to be useful in predicting the IBI?l Explain. C. Write out the appropriate regression model for this analysis. Note: This equation should contain no numbers. D. What is the least-squares regression equation for the model written in part (3.? E. Interpret each of the estimated regression coefcients in the equation from part D. in context, including the intercept. F. Create the three relevant residual plots for this linear regression model. G. Do the assumptions for the regression model hold? Explain. H. Conduct the test to determine if this model is uesful. Be sure to show all steps. I. What proportion of the variation in IBI is explained by this model? J. Conduct the hypothesis tests for each slope. Be sure to show all steps. K. Do the conclusions from part J. match your observations from part B.? L. Researchers would like to estimate the IBI for a stream that was not a part of this study. What is the predicted IBI when the area of the watershed is 55 square kilometers and is 84% forest. M. Determine the 95% prediction interval for the 113] for the stream described in part L.. N. Determine the 95% condence interval for the average IBI for streams with the characteristics given in part L.. O. Ecologists have long lobbied for protection for watershed forests because they believe that it increases the water quality. Before their next discussion with policy makers, they would like to have a estimate for the change in water quality when the percentage of watershed forest increases by 1% {assuming area of the watershed remains the same) and they ask you for an estimate with 95% condence. What values should you give them? Explain
