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The basic use of fit is best explained by a simple example:

`f(x) = a + b*x + c*x**2 fit [-234:320][0:200] f(x) ’measured.dat’ using 1:2 skip 4 via a,b,c plot ’measured.dat’ u 1:2, f(x)`

Ranges may be specified to filter the data used in fitting. Out-of-range data points are ignored. (T. Williams, C. Kelley -

gnuplot 5.0, An Interactive Plotting Program)

Linear interpolation (fitting with a line) is the simplest way to fit a data set. Assume you have a data file where the growth of your y-quantity is linear, you can use

[...] linear polynomials to construct new data points within the range of a discrete set of known data points. (from Wikipedia,

Linear interpolation)

We are going to work with the following data set, called ** house_price.dat**, which includes the square meters of a house in a certain city and its price in $1000.

```
### 'house_price.dat'
## X-Axis: House price (in $1000) - Y-Axis: Square meters (m^2)
245 426.72
312 601.68
279 518.16
308 571.50
199 335.28
219 472.44
405 716.28
324 546.76
319 534.34
255 518.16
```

Let's fit those parameters with *gnuplot*
The command itself is very simple, as you can notice from the syntax, just define your fitting prototype, and then use the `fit`

command to get the result:

```
## m, q will be our fitting parameters
f(x) = m * x + q
fit f(x) 'data_set.dat' using 1:2 via m, q
```

But it could be interesting also using the obtained parameters in the plot itself.
The code below will fit the ** house_price.dat** file and then plot the

`m`

and `q`

parameters to obtain the best curve approximation of the data set. Once you have the parameters you can calculate the `y-value`

, in this case the `x-vaule`

(```
y = m * x + q
```

the appropriate `x-value`

. Let's comment the code.

**0. Setting the term**

```
set term pos col
set out 'house_price_fit.ps'
```

**1. Ordinary administration to embellish graph**

```
set title 'Linear Regression Example Scatterplot'
set ylabel 'House price (k$ = $1000)'
set xlabel 'Square meters (m^2)'
set style line 1 ps 1.5 pt 7 lc 'red'
set style line 2 lw 1.5 lc 'blue'
set grid
set key bottom center box height 1.4
set xrange [0:450]
set yrange [0:]
```

**2. The proper fit**

For this, we will only need to type the commands:

```
f(x) = m * x + q
fit f(x) 'house_price.dat' via m, q
```

**3. Saving m and q values in a string and plotting**

Here we use the `sprintf`

function to prepare the label (boxed in the `object rectangle`

) in which we are going to print the result of the fit. Finally we plot the entire graph.

```
mq_value = sprintf("Parameters values\nm = %f k$/m^2\nq = %f k$", m, q)
set object 1 rect from 90,725 to 200, 650 fc rgb "white"
set label 1 at 100,700 mq_value
p 'house_price.dat' ls 1 t 'House price', f(x) ls 2 t 'Linear regression'
set out
```

The output will look like this.