Ideal Straight Line Fit for a Temperature Sensor Output

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The discussion focuses on calculating the ideal straight line fit for a temperature sensor's resistance output, with specific values provided for X (temperature) and Y (resistance). The calculations yield a slope (M) of approximately 0.94 and an intercept (b) of about 118.33, leading to a linear equation for resistance based on temperature. Participants suggest that rounding in calculations should be avoided and emphasize the importance of including units for temperature and resistance. Additionally, there are recommendations to use online regression software for verification and to present data in a more organized format, such as a table. Proper notation and clarity in data representation are essential for accurate analysis.
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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.
 
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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