1. If installing on Windows 8, see this knowledge base article: Statistica installation fails with Windows 8 as .NET Framework versions not installed out-of-the-box. In most cases, the installer will detect and install all the required components. See requirements listed here: .NET Framework and Visual C++ installation requirements for Statistica.

2. Follow the steps listed  in the following knowledge base article: Statistica installation fails to run to completion. Attempt to install Statistica again.

3. If all the steps in Stage 1 and Stage 2, in step 2 above, have been successfully completed and the following line appears near the end of the STATMSI.log file:
Action start : CheckCDKeyAndSerialNumber, then the .Net Framework may be corrupt. Download and run the .Net Repair Tool. See How to repair my .NET using the .NET Framework Repair Tool. If some components of the .Net Framework cannot be repaired, contact Microsoft. After successfully repairing .Net Framework components, reboot and attempt to install Statistica again.  

4. If uncertain about .Net Framework corruption, contact Statistica technical support by creating a service request. See How to request technical support through the Support Portal. Also, when creating a support case, please send in the STATMSI.log file.