Chapter 12.2, Problem 24E

The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. The article “Substrate Characteristics Affect Colonization by the Bloom-Forming Diatom Didymosphenia geminata (Aquatic Ecology, 2010: 33–40) described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data:

x	50	71	55	50	33	58	79	26
y	152	1929	48	22	2	5	35	7

x	69	44	37	70	20	45	49
y	269	38	171	13	43	185	25

1. a. Fit the simple linear regression model to this data, predict colony density when surface area = 70 and when surface area = 71, and calculate the corresponding residuals. How do they compare?
2. b. Calculate and interpret the coefficient of determination.
3. c. The second observation has a very extreme y value (in the full data set consisting of 72 observations, there were two of these). This observation may have had a substantial impact on the fit of the model and subsequent conclusions. Eliminate it and recalculate the equation of the estimated regression line. Does it appear to differ substantially from the equation before the deletion? What is the impact on r² and s?