LibreOffice follows the ODF specification. It has the formulas in OASIS Open Document Format for Office Applications (OpenDocument) Version 1.2 - Part 2: Recalculated Formula (OpenFormula) Format.

Calculating the model parameter is done by the same algorithm as used for LINEST function.

Let X denote the array of the abscissa of the data points of the series and Y the array of the associated ordinates. _n denotes an index, ^n denotes an exponent.

For case chart:regression-force-intercept=“false” the calculation can be:

For regression type:

- exponential, model y=A
*EXP(B*x): LINEST(LN(Y),X,1) results B,LN(A)
- linear, model y=Ax+B: LINEST(Y,X,1) results A,B
- logarithmic, model y=A*LN( x )+B: LINEST(Y,LN(X),1) results A,B
- polynomial, model y = A_0 + A_1 x + A_2 x^2 + … + A_n x^n : LINEST(Y,X,X^2,…,X^n,1) results A_n,…A_1,A_0
- power, model y = A*x^B : LINEST(LN(Y),LN(X),1) results B,LN(A)

For case chart:regression-force-intercept=“true” and C the value of chart:regression-intercept-value the calculation can be:

For regression type:

- exponential, model y=C
*EXP(B*X): LINEST(LN(Y/C),X,0) results B,0
- linear, model y=Ax+C: LINEST(Y-C,X,0) results A,0
- polynomial, model y = C + A_1 x + A_2 x^2 + … + A_n x^n: LINEST(Y-C,X,X^2,…,X^n,0) results A_n,…,A_1,0

You might get a better understanding, if you calculate the parameters of the trend line manually in the spreadsheet, using the LINEST function as noted above for the different trend line types.

Keep in mind, that the formula for R² as given in the linked text uses the values from the parameters of function LINEST, it does not use the values from the model directly.