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Courtney Rohatensky

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Courtney Rohatensky

on 19 July 2016

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Transcript of Courtney Rohatensky

Regression Project

During this past weekend I have spent a lot of my time working, and I had an interesting thought while I was scooping out a bowl of soup to serve to my guests. I was curious about how hot the soup is when my guest is eating it, compared to how hot it is when I initially take the scoop out of the ‘hot holding’ area. I figured that I could use my newly developed skill set and apply it to this concept.
Factors affecting the cooling rate:
- When the batch was made
- Type of dishware its placed in
- How hot the environment is
- Wind/breeze factors
- Consistency of the soup ( ie. Creamy, watery, etc. )
- Accuracy of thermometer
- Temperature of ‘hot holding’ area
- What area of the pot you scooped from (ie. Bottom-closer to burner , top-cooler area)

The reason that I had shown the two equations is because I had to determine the better fit. Therefore I looked at the coefficients of determination, r*2.
For the quadratic regression equation the coefficient is: .9951404167 which means that it is a very "good fit". However with the exponential regression equation the coefficient of determination, r 2, is
.9818915483 which means that it is also a "good fit". I believe the quadratic equation has a better fit for this case, being:
Y=(0.409370007)x*2+(-2.93987351)x+88.88193457


The quadratic regression equation is:
Y=ax*2+bx+c
Y=(0.409370007)x*2+(-2.93987351)x+88.88193457

The exponential regression equation is:
Y=a(b)*x
Y=(83.54693584)x(.9735690425)*x
Y=(84)x(.97)*x
where x stands for time.

** please note that it is to the power of 2 for the quadratic equation, and also to the power of x for the exponential equation.
The soup I studied is a thick, cream-based broth with large pieces of chicken. It is a heavy consistency compared to other soups, which I considered while conducting the project. The bowl I used for the analysis was a ceramic bowl at room temperature, however other materials could prove to have a different cooling rate. Our ‘hot holding’ area must keep our soups above 90ºC. The initial scoop came out at 92ºC, which leads me to believe it was a fresh batch right off of the stove top. After every minute, I recorded the temperature from the digital thermometer and put it into the table below.
The independent variable for this project is of course time (minutes), whereas the temperature (ºC) of remains the dependant variable.
If I want to ensure the best quality of soup for my guests, the soup should be around 70 ºC. How long do I have to get it to the table, if I want it to be the perfect temperature?

The perfect amount of time for the best of quality is 6.33 minutes and of course, the less wait time, the better. ( y= 70.084 when x=6.33 )

How hot would the soup be after 50 minutes of sitting at room temperature?

After 50 minutes at room temperature, the bowl of soup would be 22ºC. ( x=50.03 when y=21.874 )

TIME DEGREES º
(MIN) (CELSIUS)

0 92
1 89
2 84
3 79
4 76
5 74
6 71
7 69
8 67
9 65
10 63
11 61
12 59
13 57
14 56
15 53
16 52
17 51
18 50
19 48
20 47
21 46
22 45
23 44
24 43
25 42
26 41
27 40
28 39
29 38
30 38
31 37
32 36
33 36
34 35
35 35

In conclusion, the soup decreases in temperature quite drastically within the first 9-10 minutes and after that it is a gradual decline. Therefore I learnt that it is important for me to deliver the soup within the first 6 minutes or so in order to ensure that it is still hot for my guest.
temperature, (t)
time(t)
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