Ideal Straight Line Fit for a Temperature Sensor Output

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In summary: I'm not saying that you should have done that. I think that this is a simple example and your method is fine - except for the incorrect rounding. However, if you are expected to show your working, then you should present it in a neat way that makes sense to the reader.)In summary, we have data for temperature (in ºC) and the corresponding resistance of a temperature sensor. After calculating M and b for the linear regression, we can use the equation Mx + b to estimate the resistance for any given temperature. We also calculated the differences between the actual resistance and the predicted resistance (N) and found that there is some discrepancy, which may be due to measurement error or other factors. It would
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Fenrir
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Homework Statement
I am doing a distance learning course and need to find the ideal straight line of a sensor output. The sensor is a temperature sensor with an OHM output.
From a temperature range of 0-250 it has an output of 120-364ohm.
0 = 120
50 = 178
00 = 201
150 = 249
200 = 303
250 = 364

I need to generate the ideal straight line equation and values.
Relevant Equations
y = Mx + b (Least squares)
X 0 50 100 150 200 250
Y 120 178 201 249 303 364
XY 0 8900 20100 37350 60600 91000
X^2 0 2500 10000 22500 40000 62500

∑X 750
∑Y 1415
∑XY 217950
∑X^2 137500

M = (6*217950)-(750*1415) / (6*137500) - (750)^2
M = 1643 / 1750
M = 0.9388571429
M = 0.94

b = 1415-0.94*750 / 6 = 118.333333
b = 118.33

Mx + b
0.94*0 + 118.33 = 118.33
0.94*50 +118.33 = 165.33
0.94*100 +118.33 = 212.33
0.94*150 +118.33 = 259.33
0.94*200 +118.33 = 306.33
0.94*250 +118.33 = 353.33

N = Resistance - ISL

120-118.33 = 1.67
178-165.33 = 12.67
201-212.33 = -11.33
249-259.33 = -10.33
303-306.33 = -3.33
364-353.33 = -10.67

Temp 0 50 100 150 200 250
Resistance 120 178 201 249 303 364
ISL 118.33 165.33 212.33 259.33 306.33 353.33
N 1.67 12.67 -11.33 -10.33 -3.33 10.67

I'm looking at my answers and i feel like i have gotten it wrong somewhere, is there a mistake in what i have done?
Rounding only done here to simplify.

Edited to correct ∑X^2
 
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That looks ok. However, I would not have rounded M for the calculation of b.
 
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In addition to what @DrClaude said...

There is online software available, e.g. https://www.socscistatistics.com/tests/regression/default.aspx
You can compare your answer to that of the software.

Some other points:

Fenrir said:
... temperature sensor with an OHM output.
It's better to say that the output is the sensor's resistance. (The 'ohm' (##\Omega##) is the unit of resistance.)

Fenrir said:
From a temperature range of 0-250
Units are needed. For example, the temperature could be in units of ºC (degrees centigrade), ºF (degrees Farhenheit) or K (kelvin). Knowing the correct units is very important.

You may be expected to give M and b with their units.

Fenrir said:
0 = 120
.
250 = 364
It's not a good idea to write things like '0 = 120'. It's wrong. Ideally, use a table with suitable column headings.
 
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FAQ: Ideal Straight Line Fit for a Temperature Sensor Output

What is an ideal straight line fit for a temperature sensor output?

An ideal straight line fit for a temperature sensor output is a linear regression model that best represents the relationship between the sensor's output voltage (or current) and the corresponding temperature. This line minimizes the sum of the squared differences between the observed values and the values predicted by the line.

Why is it important to have an ideal straight line fit for a temperature sensor?

Having an ideal straight line fit is crucial because it ensures accurate temperature measurements. A precise linear relationship allows for easy calibration, simplifies data interpretation, and enhances the reliability of the sensor's readings in various applications.

How do you determine the ideal straight line fit for a temperature sensor?

The ideal straight line fit is determined using statistical methods such as least squares regression. This involves plotting the sensor's output against known temperature values, calculating the best-fit line that minimizes the sum of the squared residuals, and deriving the slope and intercept of the line.

What are the common challenges in achieving an ideal straight line fit for a temperature sensor?

Common challenges include sensor non-linearity, noise in the sensor output, temperature hysteresis, and environmental factors affecting the sensor's performance. Addressing these challenges often requires careful calibration, filtering techniques, and sometimes compensating for known sources of error.

How can you improve the accuracy of the straight line fit for a temperature sensor?

Accuracy can be improved by using high-quality sensors with low noise and minimal drift, performing thorough calibration over the entire temperature range, employing advanced statistical methods to refine the fit, and regularly validating the sensor's performance against known temperature standards.

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