### Solving a system of linear equations by QR Factorization Method for Temperature and Altitude Regression Model against Spontaneous-Potential

*Widowati Widowati  -  Mathematics Department, Faculty of Sciences and Mathematics, Dipongoro University, Indonesia
Agus Setyawan  -  Diponegoro University, Indonesia
Mustafid Mustafid  -  Diponegoro University, Indonesia
Muhammad Nur  -  Diponegoro University, Indonesia
Sudarno Sudarno  -  Diponegoro University, Indonesia
Udi Harmoko  -  Diponegoro University, Indonesia
Satriyo Adhy  -  Diponegoro University, Indonesia
Gunawan Gunawan  -  Diponegoro University, Indonesia
Agus Subagio  -  Physics Department, Faculty of Sciences and Mathematics, Diponegoro University, Indonesia
Heru Tjahjana  -  Diponegoro University, Indonesia
Ririn Sulpiani  -  Diponegoro University, Indonesia
Djalal Er Riyanto  -  Diponegoro University, Indonesia
Suhartono Suhartono  -  Diponegoro, Indonesia
Mochammad Abdul Mukid  -  Diponegoro University, Indonesia
Jatmiko Endro Suseno  -  Diponegoro University, Indonesia

Citation Format:
Abstract
Many real problems can be represented in the form of multiple linear regression equation. One of those is the relationship between the variables of temperature and altitude of the spontaneous-potential. In order to determine the parameters of the regression equation, the least squares method was used. From here, there was obtained the system of linear equations. In this paper, to solve systems of linear equations, the exact method was used as the exact solution is certainly better than the approached solution. The method used was the QR factorization method. At the QR factorization, the system of linear equations was written in form of matrix equation. Then, the coefficient matrix which the number of rows is m and number of columns is n with linearly independent columns was factored into the matrix Q which has the same size with the matrix A, with orthonormal columns and matrix R was upper triangular. Furthermore, by backward substitution, it could be obtained the exact solution of linear equation system. As verification of this proposed method, a case study was given using data of temperature, altitude, and spontaneous-potential in the geothermal manifestations area, Gedongsongo, Mount Ungaran Semarang. From here, it was obtained the parameters of exact multiple linear regression model which states the relationship between temperature and altitude toward the spontaneous-potential.