This paper presents the development of a new metric to improve the performance of the Dispersion of Double Differences (D³) algorithm, which detects GNSS spoofing attacks with a dual-antenna system. The new metric is based on a linear regression applied to the fractional phase double differences. The original D³ algorithm is sometimes prone to false alarms and to missed detections. The idea presented in this paper intends to overcome such limitations by leveraging on the fact that the fractional double differences are characterized by having a piecewise linear trend, with different slopes and intercepts. By evaluating the dispersion of such two parameters instead of the double difference measurements directly, it is possible to design a more robust spoofing detector. The performance of this linear regression-based method is very promising, since no cases of false alarms or of missed detections have been observed in all the performed tests.