Problem $2$: GLLS Curve Fit

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A thermistor is a resistor with a temperature$-$dependent resistance. These electronic devices are used for temperature measurement in a variety of applications. The image below shows one example of what they look like.

Diagram of a Thermistor$-$

Write a function that uses the general linear least$-$squares approach $($i$.$e$.$ QR factorization with left division$)$ to determine the best values of the constants $a,b,$ and $c$ to fit the model:

Equation model of a thermistor

to a set of data for temperature versus resistance. Your function should also calculate statistical measures to quantify the quality of the curve fit. Your function should receive a single input:

A two$-$column matrix with resistance values $($Ohms$)$ in the first column and temperature values $($Celsius$)$ in the second column.

It should return the following outputs $($in order$)$:

A $13$ row vector of the fit coefficients $a,b,$ and $c.$

The coefficient of determination $("$r$-$squared value"$)$ for the curve fit $($scalar value$).$

The standard error for the fit $($scalar value$).$

You will need to transform the mathematical model into a linear combination of basis functions to make it suitable for the general linear least$-$squares approach. You'll need to also transform the data to calculate the fit. Be sure to transform both back to their original forms before computing the curve fit quality measures.

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