Show your R work (both your input and your output) for each question below. You may find Section 22.1 in the reading useful.


Urban Runoff

Urbanization poses a major threat to stream and watershed ecosystems. One aspect of urbanization is the conversion of natural areas to land with impervious surfaces, thus increasing runoff of rain and, likely, pollutants. A University of Washington researcher recorded the percent of impervious land and the benthic index of biotic integrity (IBI) for 14 areas in the state of Washington. The IBI has been described as a measure of “the capability of supporting and maintaining a balanced, integrated, adaptive community of organisms having a species composition and functional organization comparable to that of natural habitat in the region.” In this example, the researchers were attempting to identify how the percentage of impervious surfaces in the area effects the IBI. The data for this study are below (note that much more information can be obtained at the QELP site).

imperv   60 43 43 34 27 25 21 18 11  8  8  8  7  7  5  4  2
IBI       9 11 13 23 31 31 21 23 27 37 39 29 31 43 33 35 37

Load these data into R to answer the questions below. [Note that these are the same data that you entered in a previous class exercise.]

  1. In terms of the variables of this problem, what is the equation of the best-fit line?
  2. In terms of the variables of this problem, INTERPRET the value of the slope?
  3. In terms of the variables of this problem, INTERPRET the value of the y-intercept?
  4. What is the predicted IBI for an impervious surface percentage of 30%?
  5. What is the predicted IBI for an impervious surface percentage of 70%?
  6. What is the residual if the impervious surface percentage is 10% and the IBI is 30?
  7. How much will the IBI change if the percentage of impervious surface is decreased by 25%?
  8. What is the correlation coefficient between IBI and the percentage of impervious surface?
  9. What proportion of the variability in IBI is explained by knowing the percentage of impervious surface?
  10. What aspect of this regression analysis concerns you (i.e., consider the regression assumptions)?


Red-Imported Fire Ants and Deer Fawns

Allen et al. (1997) investigated the impact of the density of red-imported fire ants (Solenopsis invicta; RIFA) on the recruitment of white-tailed deer (Odocoileus virginianus) fawns (an index of does to fawns). A modified version of their results are found in RIFA.csv (data, meta). Load these data into R and produce results that can be used to answer the questions below.

  1. What is the response variable? [Hint: Read the rest of the questions before answering this question.]
  2. What is the explanatory variable?
  3. In terms of the variables of this problem, what is the equation of the best-fit line?
  4. In terms of the variables of this problem, interpret the value of the slope.
  5. In terms of the variables of this problem, interpret the value of the intercept.
  6. If the RIFA index increases by 500, how much different do you expect fawn recruitment to be?
  7. What is the predicted fawn recruitment when the RIFA index is 500?
  8. What is the predicted fawn recruitment when the RIFA index is 1700?
  9. What is the residual when the RIFA index is 2200 and fawn recruitment is 0.3?
  10. What is the correlation coefficient between RIFA and fawn recruitment?
  11. What proportion of the variability in fawn recruitment is explained by knowing the RIFA index?
  12. Comment on the assumptions in this regression.