Data Science Asked on November 17, 2021
Short version:
How can I find a function that maps X to Y when data looks like this.
Note:
For a pair of emissivity and distance relation between temperature and
raw_thermal_data is linear.
Long Version:
I am working on a project which uses thermal(IR) camera. Now we extract temperature from sensor reading (raw thermal data )
For some reason I need to find a function that maps temperature data to raw thermal data.
Now,
temperature = F ( raw_thermal_data, emissivity, distance )
I am trying to find,
raw_thermal_data = F1 ( temperature, emissivity, distance )
For a pair of emissivity and distance relation between temperature and raw_thermal_data is linear.
Looks like for every pair of emissivity and distance, intercept of the line is different.
Any thoughts?
Not knowing the data in detail, this look like a linear model with "dummys".
A standard linear model looks like ($beta_0$ is the intercept, $beta_1$ is the slope):
$$ y = beta_0 + beta_1 x + u.$$
Now, when you have two distinct "groups" for which there is a "flag" in the data, you can assign a indicator variable or "dummy" (say $d$, a vector with =1 "true" or =0 otherwise). You can add this to your linear model:
$$ y = beta_0 + beta_1 x + beta_2 d + u. $$
$d$ introduces a separate intercept for the assigned group ($d=1$).
You can also add "interaction terms" to allow for a separate slope for group $d$ by simply multiplying $x$ and $d$.
$$ y = beta_0 + beta_1 x + beta_2 d + beta_3 x d + u. $$
Note that since there already is one intercept in the model (the $beta_0$), you can only add "contrasts" to the intercept. So when you have $i$ groups for which you want to have an individual intercept, you would add $i-1$ indicators/dummys to the model. For the "reference group", the intercept will be $beta_0$ and for the group which is identified by the "dummy" ($d$ above), the intercept would be $beta_0 + d$.
Answered by Peter on November 17, 2021
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