The index of biotic integrity (IBI) is a measure of the water quality in streams
ID: 3313523 • Letter: T
Question
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. The data data226.dat gives the data for IBI and the area of the watershed in square kilometers for streams in the original sample with area less than or equal to 70km2. (a) Use numerical and graphical methods to describe the variable IBI. Do the same for area. (Round your answers for x to two decimal places and your answers for s to three decimal places.) Jx IBI area: (b) Run the simple linear regression and summarize the results. (Let x- area and y -IBI. Round your slope, intercept, and r to three decimal places. Round F to two decimal places and your P-value to four decimal places.) F= Is area of watershed a good predictor for IBI at the 5% significance level? Yes, the area of watershed is a good predictor for IBI O No, there is insufficient evidence to say the area of watershed is a good predictor for IBI.Explanation / Answer
a) From the given data
Descriptive Statistics: Area, IBI
Variable Mean StDev
Area 28.29 17.71
IBI 62.08 20.18
b)
The regression equation is
IBI (Y) = 49.1 + 0.459 Area (X)
F=9.12
P= 0.004
r = 0.403
c) correct answer: yes, the are of watershed is a good predictor for IBI
d) interpret of intercept:
Correct answer: option (a)
e) Interpret of slope
Correct answer: Option (B)
f) P-value
Correct answer: Option (A)
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