Question

The data set below shows the temperature, in degrees Fahrenheit, of a mug of tea compared tothe time in minutes after being poured out of the tea kettle. An exponential regression wasperformed on this data to obtain the model y - 174.4(0.987)*. Create a residual plot andexplain why the model is or is not good fit for this data.

Answer 1

Given the model of the Exponential Regression:

$y=174.4(0.987)^x$

By definition:

$Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value$

You can see in the table the observed y-values (the temperature in Fahrenheit)

In order to find the Predicted y-values, you need to substitute all the x-values given in the table (the time in minutes) into the equation and then evaluate. You get:

$y=174.4(0.987)^5\approx163.35$$y=174.4(0.987)^8\approx157.07$$y=174.4(0.987)^{11}\approx151.02$$y=174.4(0.987)^{15}\approx143.32$$y=174.4(0.987)^{18}\approx137.80$$y=174.4(0.987)^{22}\approx130.77$$y=174.4(0.987)^{25}\approx125.74$$y=174.4(0.987)^{29}\approx119.33$$y=174.4(0.987)^{32}\approx114.73$$y=174.4(0.987)^{35}\approx110.32$

Now you have these points:

$(5,163.35),(8,157.07),(11,151.02),(15.143.32)(18,137.800),(22,130.77),(25,125.74),(29,119.33),(32,114.73),(35,110.32)$

Therefore, you can plot them on the Coordinate Plane:

By definition, when the residual plot shows a pattern, a non-linear regression model is appropriate for the data. Therefore, the Exponential Regression Model is a good fit.

Hence, the answer is:

- Residual Plot:

- First option.