posted by Brittany on .
Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5º C after 3 minutes; 90º C after 5 minutes, 84.8 C after 9 minutes; 70.2º C after 18 minute; 54.4º C after 30 minutes; 42.5ºC after 37 minutes; and 24.9º C after 48 minutes. Perform a linear regression on this data to complete the following items.
1.) What does the value of the correlation coefficient tell you about correlation of the data?
2.) Write the equation of the best-fitting line. (Round to the nearest thousandths.)
3.) On average, how much does the temperature decrease every five minutes?
4.) If Natalie's solution is expected to freeze at -7º C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction).
Given the data, you should get a piece of graph paper (or use excel or some other graphing program) and plot the points with time on the x-axis and temperature on the y-axis. You will probably get a graph that looks something like this:
(I don't know how to draw a better graph than this here.)
Now, to determine the equation of the line, if you do this in a graphing program, tell it to insert a trend line and to show you the equation of the line. If you are doing it on paper, you need to draw in the best line and extend it to time = 0 (the y-intercept). To calculate the slope, pick two points on the line, and calculate the slope as y2-y1 / x2-x1 = slope (your slope should have a negative value).
The equation of the line is then y = slope (x) + y intercept
When I plotted your data, the equation came out to be: y = -1.5908x + 101.33
For your first question, plug -7 in for y and calculate x, and you've got it. My calculation comes out to 68 minutes