Constructing Equations from Points

[Dominic Luciano]

Hi guys, new here. Thank you for reading my post. I'm posting today because although I'm an engineer, I have some brain tumors that have impeded my ability to process most math above basic algebra (despite the fact that prior I'd gone all the way through stats in college). It didn't really start until I was in about that last year of college, and the older I get the worse it gets. Makes my job hard sometimes, but generally I honestly don't run into this kind of math often. The funny part is I was told the tumors could very well have stimulated other parts of my brain which is why I have a higher than normal aptitude for a ton of other things. Give and take I guess. But enough about me; down to business ;)

I'm trying to write some equations based off of some data points that I have for a relatively easy project (the engineering side). Currently I'm in the programming stage, so this is all that's really left.

The project pulls the temperature from a resistive probe in the engine block of a 4Runner (12V in, lower voltage out; read that voltage and the difference in V is the temp). That information is translated down to 5V by a voltage divider (a really high wattage one at that) and a Zener diode for safety. Then the Analog to Digital Converter (ADC) on a Mega328P reads that voltage and translates that into the duty cycle of a PWM controlling a 120A MOSFET controlling the radiator fan. But if I can't get the right equation, then this becomes trash and doesn't work.

According to Excel, the "Power" trendline for my data is: y = 119.8x^(-0.881)

This is perfect until it gets to the higher voltages where is gets off course and skyrockets. Those higher voltages are VERY close and VERY important to stay on track with, and this equation veers off like a secondhand rocket above 3V.

So if anyone has some time and would be willing, it would be a huge help if someone could write up an equation for me with these data points. I'm having serious trouble and getting really frustrated with myself.

Resistance is the x value, and Voltage is the y value. As I stated, everything above ~3V is pretty important as this is where the magic starts to happen.

Thank you to anyone who helps. It means the world to me, seriously it does. Have a good night, guys ;)

 

[FactChecker]

The power curve fit assumes that the random errors are in the form of multipliers other than 1.0. Suppose you had an error of 0.1 where the model value is 1.0 and an error of 100 where the model value is 1000. Those errors would both be 10% errors so both are multipliers of 1.1, They would have equal influence in estimating the model parameters. If you want a better fit to the high voltages, you need to model the process as a linear model, not a power..

 

[Dominic Luciano]

The power curve fit assumes that the random errors are in the form of multipliers other than 1.0. Suppose you had an error of 0.1 where the model value is 1.0 and an error of 100 where the model value is 1000. Those errors would both be 10% errors so both are multipliers of 1.1, They would have equal influence in estimating the model parameters. If you want a better fit to the high voltages, you need to model the process as a linear model, not a power..

I can't model it as a linear function. It's the way the numbers have fallen based off of real-world testing

 

[Svein]

At first glance it looks like the curve for an NTC (Negative Temperature Coefficient) resistor. Check out https://en.wikipedia.org/wiki/Thermistor.

 

[Dominic Luciano]

At first glance it looks like the curve for an NTC (Negative Temperature Coefficient) resistor. Check out https://en.wikipedia.org/wiki/Thermistor.

Yes, that's correct. It's an Import Direct Temperature Sensor for a Toyota 4Runner