The index of biotic integrity (IBI) is a measure of the water quality in streams
ID: 3313848 • 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.) 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.) 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. No, there is insufficient evidence to say the area of watershed is a good predictor for IBI Interpret the intercept. The value of IBI when watershed area is 0 The area of watershed when IBI value is o The increase in IBI when the watershed area is increased by one unit The increase in the watershed area when IBI is increased by one unit Interpret the slope. The value of IBI when watershed area is 0 The increase in IBI when the watershed area is increased by one unit The area of watershed when IBI value is 0 The increase in the watershed area when IBI is increased by one unitExplanation / Answer
a)
Mean of area = 28.29
Standard deviation of area = 17.714
Mean of ibi = 62.08
Standard deviation of ibi = 20.184
b)minitab output
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3179 3179.2 9.12 0.004
area 1 3179 3179.2 9.12 0.004
Error 47 16377 348.4
Lack-of-Fit 28 8677 309.9 0.76 0.746
Pure Error 19 7699 405.2
Total 48 19556
Model Summary
S R-sq R-sq(adj) R-sq(pred)
18.6665 16.26% 14.48% 9.73%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 49.09 5.06 9.70 0.000
area 0.459 0.152 3.02 0.004 1.00
Regression Equation
ibi = 49.09 + 0.459 area
y=49.09+0.459 X
F = 9.12
P = .0041
The value of R is: 0.403
C) Is area of watershed a good predictor for IBI at the 5% significance level? (Select one of the following below)
Answer: Yes, the area of watershed is a good predictor for IBI.
D) Interpret the intercept. (select one of the following below)
Answer:
The value of IBI when watershed area is 0.
E) Interpret the slope. (Select one of the following below).
Answer:
The increase in IBI when the watershed area is increased by one unit.
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