Faulty Interaction Localization (FIL) is a process to identify which combination of input parameter values induced test failures in combinatorial testing. An accurate and fast FIL provides helpful information to fix defects causing the test failure. One type of conventional FIL approach, which analyzes test results of whole test cases and estimates the suspiciousness of each combination, has two main concerns; (1) the accuracy is not enough, (2) the huge time cost is sometimes needed. In this paper, we propose two novel approaches to improve those concerns. FROGa attempts to estimate suspiciousness more accurately using logistic regression analysis. FROGb attempts to estimate failure-inducing combinations at high speed by estimating the subsets of them using logistic regression analysis and exploring just their supersets. Through evaluation experiments using a large number of artificial test results based on several real software systems, we observed that FROGa has very high accuracy, and FROGb can drastically reduce time cost for targets that have been difficult to complete by the conventional method.