The index of biotic integrity (IBI) is a measure of the water quality in streams
ID: 3330361 • 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.)
(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?
A) Yes, the area of watershed is a good predictor for IBI.
B) No, there is insufficient evidence to say the area of watershed is a good predictor for IBI.
Interpret the intercept.
A)The value of IBI when watershed area is 0
B) The increase in IBI when the watershed area is increased by one unit
C) The area of watershed when IBI value is 0
D) The increase in the watershed area when IBI is increased by one unit
Interpret the slope.
A) The area of watershed when IBI value is 0
B) The increase in IBI when the watershed area is increased by one unit
C) The value of IBI when watershed area is 0
D) The increase in the watershed area when IBI is increased by one unit
Interpret the P-value.
A) If the P-value is less than 0.05 then we can conclude that the watershed area is a good predictor for IBI.
B) If the P-value is less than 0.05 then we can conclude that the watershed area is a bad predictor for IBI.
C)If the P-value if less than 0.05 then we can conclude that the intercept is 0
D) If the P-value is greater than 0.05 then we can conclude that the watershed area is a good predictor for IBI.
IBI: x = s = area: x = s =Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: ibi
Independent Variable: area
ibi = 49.086473 + 0.45942485 area
Sample size: 49
R (correlation coefficient) = 0.40319897
R-sq = 0.16256941
Estimate of error standard deviation: 18.666456
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) IBI:
x = 62.08
s = 20.184
Area:
x = 28.29
s = 17.714
b) y = 49.086 + 0.459 x
F = 9.12
P = 0.0041
r = 0.403
Yes, the area of watershed is a good predictor for IBI. Option A is correct.
Intercept interpreation: Option A is correct.
Slope interpretation: Option B is correct.
p - value interpretation: Option A is correct.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 49.086473 5.0615836 0 47 9.6978488 <0.0001 Slope 0.45942485 0.15209696 0 47 3.020605 0.0041Related Questions
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