Question

The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.17 + 0.095x.
A) What is the true average flow rate for a pressure drop of 10 in. and drop of 15 in.?
B) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?
C) What is the average change in flow rate when pressure drop decreases by 5 in.?

Answer 1

Answer:

A. 0.78 and 1.255.

B.  0.095

C. -0.475

Step-by-step explanation:

The given regression line is

y=-0.17+0.095x

A.

The true average flow rate for a pressure drop of 10 inch can be computed by putting x=10 in above equation.

y=-0.17+0.095*10

y=-0.17+0.95

y=0.78

The true average flow rate for a pressure drop of 10 inch is 0.78.

The true average flow rate for a pressure drop of 15 inch can be computed by putting x=15 in above equation.

y=-0.17+0.095*15

y=-0.17+1.425

y=1.255

The true average flow rate for a pressure drop of 15 inch is 1.255.

B.

The slope represents average change in y due to unit change in x.

So, the true average change in flow rate associated with a 1 inch increase in pressure drop is 0.095(1)= 0.095.

C.

When pressure drops decreases by 5 in. then the average change in flow rate is 0.095(-5)=-0.475.

Answer 2

The flow rate in the device is an illustration of average rates.

• The true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectively
• The true average flow rates associated to a 1 in pressure increment is 0.095
• A decrement of -5 in is out of the domain of the function

The function is given as:

$\mathbf{y = -0.17 + 0.095x}$

(a) The true average flow rate when pressure drops 10 and 15 in

When x = 10, we have:

$\mathbf{y = -0.17 + 0.095 \times 10}$

$\mathbf{y = 0.78}$

When x = 15, we have:

$\mathbf{y = -0.17 + 0.095 \times 15}$

$\mathbf{y = 1.255}$

Hence, the true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectively

(b) The true average flow rate when pressure increases by 1 in

This simply represents the slope of the function.

The function is given as:

$\mathbf{y = -0.17 + 0.095x}$

A linear regression equation is represented as:

$\mathbf{y = b + mx}$

Where m represents the slope

By comparison:

$\mathbf{m = 0.095}$

Hence, the true average flow rates associated to a 1 in pressure increment is 0.095

(c) The average change in flow rate when pressure drops decreases by 5 in

The domain of the function is given as:

$\mathbf{x = 5\ to\ 20}$

A decrement of -5 in means: x = -5

This is out of the domain of the function

Hence, the average change at a decrement of 5 in cannot be calculated

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