Submitted by **Moewillgo** t3_126ft2b
in **explainlikeimfive**

[removed]

Submitted by **Moewillgo** t3_126ft2b
in **explainlikeimfive**

[removed]

This is a very nice example.

You can also tell from the conversion formula (which is the formula behind that graph, too) that the relationship is linear. Namely...

>F = 1.8 * C + 32 (or C = 5/9 * F - 32)

...is a classic a * x + b linear formula.

E: switched F and C originally.

>C = 1.8 * F + 32

Actually, it's F = 1.8 * C + 32

Cool, now I am confused.

I described the conversion of celsius to fahrenheit but accidentally flipped the F and C in the formula. It's corrected now, and I added the opposite conversion for good measure.

Oh yes, I switched them up. Lemme fix that.

I think I get it now, thank you (:

Linear doesn't mean the scale is 1:1. Visually, if you plot the corresponding C and F measurements (say the C on the horizontal axis and F on the vertical), you get a straight line. This is a "linear" relationship between F and C.

It does not mean that 0C = 0F nor does it mean a 1 degree difference in F equals a 1 degree difference in C. It means a proportional change in one results in an identical proportion change in another.

The relationship between Celsius and Fahrenheit is linear because any change in Celsius is the same change in Fahrenheit multiplied by a constant (1.8).

That means, any change in temperature by 1 degree Celsius is the equivalent of a 1.8 degree change in Fahrenheit.

delta F = delta C x 1.8

Yes, if you look at the liquid range of water you see it's 32-212 if F, or 0-100 in C. (212-32)/(100-0) shows that there's 1.8 change in F for every change of 1C.

There is a linear relationship. Milestones are simplistically related to water - freezing (0C° = 32F°) and boiling (100C° = 212F°). Both C° and F° are calibrated according to this 0/32 an 100/212 scale.

Other users have shown more detail on the relationship but didn't explicitly mention water / freeze / boil.

The easiest way to picture it is the correlation between meter and centimeter.

1 meter is 100 centimeters, but 2 meters are not 101 centimeters but 200. The relationship is linear because you use a linear function to convert from one unit to the other. In this case it's `meter = 100 cm`

.

In case fahrenheit it's more complex to calculate in your head, but simple if written down: `Celsius = (Fahrenheit - 32) x 5/9`

.

To imagine a non-linear correlation you can think of something like how the amount of chocolate you eat relates to your enjoyment.

You eat a bar of chocolate, that's cool. You eat two, it's better. But as you keep eating more and more you start to get full and by the time you eat your 25th bar of chocolate you'll want to puke. So if you'd want to illustrate it on a chart, the line would start to rise and quickly drop at a point the more chocolate you eat.

The relationship would be linear if your enjoyment would increase by the same logic regardless of how many chocolate you ate (or more precisely, if there was a linear function that you could use to calculate it).

Edit: clarification

>linear correlation means that the degree difference should be the same, like if the difference between -5 and 5 is ten then the difference in Fahrenheit should also be 10, but it's not, which confuses me severely

Linear correlation means "if you change the °C by 10, then no matter what the original °C was, the °F changes by the same amount (not necessarily 10) each time".

Or, more simply, if you plotted °F against °C, the graph would be a straight line.

The slope of that line doesn't have to be 1.

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OrbitalPetet1_je8xuhg wroteThere is a linear correlation, but the origin is not at 0.

https://qph.cf2.quoracdn.net/main-qimg-7df15e6faf5f599060c6884fc88d39d7-pjlq

Both scales have a constant linearity to them, and 1 degree Celsius increase is always a 1.8 degree Farenheit increase.

This graph plots one against the other, as you can see showing a linear correlation. https://d1uvxqwmcz8fl1.cloudfront.net/tes/resources/11829524/ff0efc69-c7a4-4963-ba86-c733ac6602a3/image?width=500&height=500&version=1541452521288