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Question: the index of biotic integrity ibi is a measure of...

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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.

​Below is the data. Each number alternates between the area and the ibi. please solve the bolded questions below as well.

area ibi 21 60 29 58 31 74 32 92 34 81 34 52 49 94 52 73 2 65 70 70 6 46 28 31 21 52 59 90 69 55 47 51 8 35 8 67 58 85 54 77 10 53 57 79 18 85 19 19 39 89 49 68 9 40 5 24 14 52 9 34 23 80 31 73 18 80 16 32 21 69 32 80 10 57 26 1 9 74 54 58 12 57 21 69 27 60 23 61 26 77 16 61 26 78 26 72 28 52

(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: x = ?
s = ?
area: x = ?
s = ?


(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.)

y = ? + ? x
F = ?
P = ?
r = ?


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 increase in IBI when the watershed area is increased by one unit

The value of IBI when watershed area is 0    

The increase in the watershed area when IBI is increased by one unit

The area of watershed when IBI value is 0


Interpret the slope.

The value of IBI when watershed area is 0

The area of watershed when IBI value is 0    

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 P-value.

If the P-value is greater than 0.05 then we can conclude that the watershed area is a good predictor for IBI.

If the P-value if less than 0.05 then we can conclude that the intercept is 0    

If the P-value is less than 0.05 then we can conclude that the watershed area is a bad predictor for IBI.

If the P-value is less than 0.05 then we can conclude that the watershed area is a good predictor for IBI.

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