Time	Temperature [C]
12:00 AM	15
1:00 AM	16
2:00 AM	15
3:00 AM	15
4:00 AM	15
5:00 AM	14
6:00 AM	14
7:00 AM	13
8:00 AM	13
9:00 AM	14
10:00 AM	13
11:00 AM	14
12:00 PM	15
1:00 PM	16
2:00 PM	18
3:00 PM	20
4:00 PM	21
5:00 PM	21
6:00 PM	21
7:00 PM	20
8:00 PM	19
9:00 PM	17
10:00 PM	16
11:00 PM	15

You can download here the recorded temperatures in Montreal on June first 2010 in an excel table). Fit the data set using the model T=a, + ay sin 27t + a2 cos 2nt where T is the temperature in degree Celsius and t is the time of the temperature measurement in fraction of days (e.g. at 12PM (noon) t = 0.5). Use 16 digits in your calculations and give the answers with at least 5 significant digits ao = ai = a2 = The root mean square error RMSE is