A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be amount of eroded soil = 0.4 + 1.3x (where x is flow rate) The correlation between amount of eroded soil and flow rate would be:

Question

Mathematics

Digger

19 April, 16:46

A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be amount of eroded soil = 0.4 + 1.3x (where x is flow rate) The correlation between amount of eroded soil and flow rate would be:

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Ariella · Answer 1

We are given the specific equation:

amount of eroded soil = 0.4 + 1.3 x

where x is the flow rate

A linear equation has a general formula in the form of:

y = m x + b

where m is the slope and b is the y intercept of the equation

If we compare this with our specific equation, we can see that the slope and y intercept are both positive with values:

m = 0.4

b = 1.3

Therefore this only means that as the flow rate increases, the amount of eroded soil also increases.

Hence the correlation must be positive but we cannot solve for the exact value since we need the data for x and y.

Answer:

positive, but we cannot say what the exact value is