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tokens: I -band model at 1% significance. This could be due to blending problems and also to the lack of extinction correction in OGLE-IV data. To perform stability tests, the data are split by dummy variables into two data sets around P = 3.85 days (OGLE-II) and P = 3.5877 days (OGLE-IV), so as to have about half of observations in each set. No evidence of structural breaks is found, because the P -values obtained, by testing versus the hypothesis that at least one of them is not 0 in Equation ( 32 ), are 0.601 (OGLE-II) and 0.453 (OGLE-IV) in the V -band, and 0.810 (OGLE-II) and 0.267 (OGLE-IV) in the I -band. Models explain about 61% and 68% of variability in the V - and I -bands respectively (OGLE-II), and 54% and 65% of variability in the V - and I -bands respectively (OGLE-IV). The estimated parameters of the models and their confidence intervals are reported in Table 6 . Results for the I -band are shown only for information purposes because of their specification problems. Table 6 Optical Leavitt Law for the LMC Note. The reported β estimators are those given by Equations ( 26 ) and ( 27 ). They were obtained by using the MM -regression. Confidence intervals are reported at 95%. The last columns report the values of zero point and the slope obtained by Soszyński et al. ( 2015 ) using the sigma-clipping algorithm and OLS over OGLE-IV data. The OGLE-II and OGLE-IV MM -estimators obtained in the V -band and their respective confidence intervals include at the OLS estimators reported by Udalski ( 2000 ) and Soszyński et al. ( 2015 ). The OGLE-IV LMC data were also split into two around P = 10 days by Equation ( 32 ). No evidence of a structural break is found in the slope, because the P -value obtained is 0.705. However, the zero-point adjustment is significant. As a result, there is evidence of two parallel regression lines. The SMC slope tests for models ( 26 ) and ( 27 ) are significant because the P -values obtained are less than 0.0001 for the V - and I -bands (OGLE-II, OGLE-IV). However, these models show problems. The test of Godfrey and Orme finds enough evidence of specification problems because the P -values obtained are less than 0.0001 for the V - and I -bands (OGLE-II, OGLE-IV). To perform stability tests, data are split around 2.0039 days (OGLE-II) and 1.9429 days (OGLE-IV) so as to have about half of observations in each data set. Enough evidence of structural breaks is found: P -values are less than 0.0001 in both bands (OGLE-II) when testing versus the hypothesis that at least one of them is not 0 in Equation ( 32 ). Besides, when individual significance tests are performed for and , the P -values obtained are less than 0.0001 for in both bands, and 0.0322 and 0.0082 for in the V -band and I -band respectively. As a result, in both bands there are two regression lines at 5% significance (OGLE-II). Unlike OGLE-II models for the SMC, there is not enough evidence to support the idea that OGLE-IV model parameters for the slope are