# Increasing monthly temperatures - don't understand the question

• May 1st 2009, 04:49 PM
Shukie
Increasing monthly temperatures - don't understand the question
I'm doing an assignment in Mathematica and I need some help understanding the question. I have a datasheet with temperatures for each month for the last 108 years:

http://www.knmi.nl/klimatologie/maan...geg_260_tg.txt

Question 3 was:

"Determine the average temperature of each month over the period 1901-2008. Make a table with two columns and twelve rows, showing the average temperature for each month."

That was easy enough. Now comes question 4:

"Same as question three, but now we assume a linear warming. That means for each month the average temperature will be fit by the function $t_{average,i}[x] = a_i + b_i(x -2008)$. In this function, i goes from 1 to 12 (from january to december) and x from 1901 to 2008. Your table will now have three columns. What is the meaning of $a_i$ and $b_i$? What are their dimensions?"

This question confuses me and if it confuses you too it might be due to my shoddy translation. Anyway, what exactly am I supposed to put in the third column? I assume I will have to calculate the values of a_i and b_i? So the third column will have twelve rows of something like: 5 + 6(1901 - 2008)? If so, how do I calculate those values for a_i and b_i?
• May 2nd 2009, 09:59 PM
CaptainBlack
Quote:

Originally Posted by Shukie
I'm doing an assignment in Mathematica and I need some help understanding the question. I have a datasheet with temperatures for each month for the last 108 years:

http://www.knmi.nl/klimatologie/maan...geg_260_tg.txt

Question 3 was:

"Determine the average temperature of each month over the period 1901-2008. Make a table with two columns and twelve rows, showing the average temperature for each month."

That was easy enough. Now comes question 4:

"Same as question three, but now we assume a linear warming. That means for each month the average temperature will be fit by the function $t_{average,i}[x] = a_i + b_i(x -2008)$. In this function, i goes from 1 to 12 (from january to december) and x from 1901 to 2008. Your table will now have three columns. What is the meaning of $a_i$ and $b_i$? What are their dimensions?"

This question confuses me and if it confuses you too it might be due to my shoddy translation. Anyway, what exactly am I supposed to put in the third column? I assume I will have to calculate the values of a_i and b_i? So the third column will have twelve rows of something like: 5 + 6(1901 - 2008)? If so, how do I calculate those values for a_i and b_i?

You calculate the $a_i$ and $b_i$ using linear regression, and now your table will have as columns: month, average temp, average temp from the regression model.

The dimensions of $a_i$ are $\text{[C]}$ (degrees celsius - I would normally have used $\text{[K]}$ here myself), and of $b_i$ are $\text{[C][T]}^{-1}$ (degrees celsius per year)

CB
• May 3rd 2009, 06:12 AM
Shukie
Thanks for the help!