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Nonlinear Regression Models Assignment

The following data shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180*.

Time Temperature *F
0 179.5
5 168.7
8 158.1
11 149.2
15 141.7
18 134.6
22 125.4
25 123.5
30 116.3
34 113.2
38 109.1
42 105.7
45 102.2
50 100.5




1. What is the linear equation of the model?
2. What are the nonlinear equations of the model? (Quadratic, Cubic)
3. What is the significance level of each model? What do they mean?
4. What are the R Square values for each model? What do they mean?
5. Which model seems to provide the best fit? Explain?
 Mar 17, 2014
 #1
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Plot the temperatures against time on a graph, like below. Then obtain and plot the best-fit lines (linear, quadratic, cubic). See below (I've not plotted the cubic below because it obscures the quadratic). You should really spend time learning about curve-fitting and the statistics of curve fitting - see http://en.wikipedia.org/wiki/Curve_fitting for starters, for example.

CurveFits.PNG

Incidentally, this is all linear regression not non-linear regression.
 Mar 17, 2014

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