Fahrenheit and Celsius conversion – linear regression on perfect data

Fahrenheit and Celsius degrees are related in a linear way. Given a table with pairs of both Fahrenheit and Celsius degrees, we can estimate the constants to devise a conversion formula from degrees Fahrenheit to degrees Celsius, or vice versa:

⁰F	⁰C
5	-15
14	-10
23	-5
32	0
41	5
50	10

Analysis from first principles

We would like to derive a formula for converting F (degrees Fahrenheit) to C (degrees Celsius), as follows:

Here, a and b are the constants to be found. A graph of the 

 function is a straight line and, thus, is uniquely determined by two points. Therefore, we actually only need two points from the table, say, pairs (F1,C1) and (F2,C2). Then, we will have the following:

Now, we have the following:

 

.

Therefore, we have the following:

Here, let's take the first two pairs (F1,C1)=(5,-15) and (F2,C2)=(14,-10). This will give us the following:

Therefore, the formula to calculate degrees Celsius from degrees Fahrenheit is as follows:

Let...