natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5C after 3 minutes; 90C after 9 minutes; 70.2C after 18 minutes; 54.4C after 30 minutes; 42.5C after 37 minutes; and 24.9C after 48 minutes. Perform a linear regression on this data to complete the following items.
-what does the value of the correlation coefficient tell you about the correlation of the data?
-write the equation of the best fitting line.(round to the nearest thousandths.)
-on average how much does the temperature decrease every five minutes?
-if natalies solution is expected to free at -7C, how many minutes into the experiment should the solution freeze? (show work that supports your prediction and round to the nearest minute.)
Using the time t as the independent variable and the temperature c as the dependent variable we can use a graphing utility or spreadsheet utility to compute the linear regression:
`c=100.407-1.565t` with `r~~-.997` and `r^2~~.994`
(a) Since r<0 there is a negative correlation. Since the correlation is almost -1, it is a very strong correlation.
(b) `c=100.407-1.565t` where c is degrees Celsius and t is time in minutes.
(c) There is a drop of 1.565 degrees every minute so the 5-minute average is approximately 7.825 degrees Celsius.
(d) Setting c=-7 and solving for t we get:
Thus the time is approximately 69 minutes to cool to `-7^@C` .