Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5°C after 3 minutes; 90°C after 5 minutes, 84.8°C after 9 minutes; 70.2°C after 18 minutes; 54.4°C after 30 minutes; 42.5°C after 37 minutes; and 24.9°C after 48 minutes.
It says to perform a linear regression

1) what does the value of the correlation coefficient tell you about the correlation of the data?

2) write the equation of the best-fitting line. (Round to the nearest thousands)

3) on average how much does the temperature decrease every five minutes?

4) if Natalie's solution is expected to freeze at -7°C, how many minutes into the experiment should the solution freeze?

I think I got the right answers I just want to make sure once again. Please help if you can. All help is appreciated. I suck at this algebra stuff. Thank you very much

Question

13-08-2017
Mathematics

contestada

Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5°C after 3 minutes; 90°C after 5 minutes, 84.8°C after 9 minutes; 70.2°C after 18 minutes; 54.4°C after 30 minutes; 42.5°C after 37 minutes; and 24.9°C after 48 minutes.
It says to perform a linear regression

1) what does the value of the correlation coefficient tell you about the correlation of the data?

2) write the equation of the best-fitting line. (Round to the nearest thousands)

3) on average how much does the temperature decrease every five minutes?

4) if Natalie's solution is expected to freeze at -7°C, how many minutes into the experiment should the solution freeze?

I think I got the right answers I just want to make sure once again. Please help if you can. All help is appreciated. I suck at this algebra stuff. Thank you very much

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Аноним Аноним · Answer 1 · 2017-08-23T06:50:38+02:00

Tabulate the data as shown below.

time, min Temp, °C
------------- -------------
3 93.5
5 90.0
9 84.8
18 70.2
30 54.4
37 42.5
48 24.9

Graph the data to observe the trend of the data. Then use the graphic calculator to determine the regression line. You may also use the Microsoft Excel spreadsheet to obtain the result.

Parts 1) and 2)
The regression line has the equation
y = 98.019 - 1.5056x
where
x = time, minutes
y = temperature, °C

The correlation coefficient of R² = 0.999 (virtually equal to 1) means that the data fits a least square straight line perfectly.

Part 3)
The slope of the straight line is -1.5056.
It represents the decrease in temperature per minute.

Answer: The temperature decreases by about 1.5 °C every minute.

Part 4)
To attain a temperature of -7°C, the equation says that
98.019 - 1.5056x = -7
1.5056x = 98.019 + 7
x = 69.75 min = 70 min (approximately)

Answer: The solution freezes after about 70 minutes