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Chapter 13: Problem 2

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 population regression line \(y=-0.12+0.095 x\). a. What is the mean flow rate for a pressure drop of 10 inches? A drop of 15 inches? b. What is the average change in flow rate associated with a 1 inch increase in pressure drop? Explain.

Short Answer

Expert verified
a. The mean flow rate for a pressure drop of 10 inches is \(0.83\) and for a drop of 15 inches is \(1.305\). b. The average change in flow rate associated with a one-inch increase in pressure drop is \(0.095\).

Step by step solution

01

Calculate the mean flow rate for a pressure drop of 10 inches

To calculate the mean flow rate for a pressure drop of 10 inches, substitute \(x = 10\) into the equation \(y=-0.12+0.095 x\) which gives \(y=-0.12+0.095 * 10\). Solving this, it is found that the mean flow rate is \(0.83\).
02

Calculate the mean flow rate for a pressure drop of 15 inches

To calculate the mean flow rate for a pressure drop of 15 inches, substitute \(x = 15\) into the equation \(y=-0.12+0.095 x\) which gives \(y=-0.12+0.095 * 15\). Solving this, the mean flow rate is observed to be \(1.305\).
03

Determine the average change in flow rate for a 1-inch increase in pressure drop

The coefficient of the variable, x, in the linear regression model gives the change in the dependent variable (y) for a unit change in the independent variable (x). Therefore, the average change in flow rate associated with a one-inch increase in pressure drop is 0.095.

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Most popular questions from this chapter

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