Question

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 4.40 − 0.01x and σ = 0.08. (a) What is the expected change in reaction time for a 1°F increase in temperature? For an 8°F increase in temperature?

Answer 1

Answer:

The expected change in reaction time for a 1°F increase in temperature is 4.39 hours.

The expected change in reaction time for a 8°F increase in temperature is 4.32 hours.

Step-by-step explanation:

The simple linear regression line is used to determine the changes in the dependent variables when the independent variable is changed.

The general form of the simple linear regression line is:

$y=\alpha +\beta x$

The simple linear regression model for the reaction time of a certain chemical process based on the temperature (°F) in the chamber in which the reaction takes place is:

$y=4.40-0.01\ x$

Here,

y = reaction time (in hours)

x = temperature (°F)

Compute the expected change in reaction time for a 1°F increase in temperature as follows:

$y=4.40-0.01\ (1^{\text{o}})$

  $=4.40-0.01\\=4.39\ \text{hours}$

The expected change in reaction time for a 1°F increase in temperature is 4.39 hours.

Compute the expected change in reaction time for a 8°F increase in temperature as follows:

$y=4.40-0.01\ (8^{\text{o}})$

  $=4.40-0.08\\=4.32\ \text{hours}$

The expected change in reaction time for a 8°F increase in temperature is 4.32 hours.