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tokens: types is generally similar throughout. That said, we note two small biases: (i) cool stars (K stars and the only M star of the sample) have in general a small presence in the subsamples; and (ii) when the density is in the relation, there is a larger contribution of F-stars and G-stars, since asteroseismology provides most of its data for these stellar types. Table 8 Percentage of Stars in the Different Subsets Used for Obtaining the Regressions with Different Spectral Types 5.2. Linear Regression Consistency In addition to using R 2 , relative accuracy, and relative precision as the main statistics for studying the quality of the regressions, we have also developed additional consistency tests to ensure that the linear regressions are representative of the observational data. In Figure 7 , we show q – q plots of the 38 selected relations selected in a form to show whether the standardized residuals are normally distributed. The ordered standardized residuals are plotted on the ordinate of each plot, while the expected order statistics from a standard normal distribution are on the abscissa. Points close to the straight line are consistent with a normal distribution. In this figure we can see that all the relations do in general follow this straight line. Therefore, the use of linear regression is justified. Only in a few cases are there extreme departures from this straight line, but in general the departures are not statistically significant. Figure 7. q – q plots of the 38 relations. See the text for details. In Figure 8 we present the residuals as a function of the fitted values of these 38 relations. Any clear trend in these residuals can be a signature of inaccurate or inefficient regression. We have also added a LOESS (local polynomial regression) curve to guide the eye. In this figure we can see that, in general, there are no clear trends in the distributions of the residuals. In every plot, the main body of points is randomly distributed around the value zero. There are a few extreme cases, but they contain only a small percentage of the observational set. The impact of these values on the regression coefficients is analyzed in the next figure. Figure 8. Residuals vs. the fitted values of the 38 relations. The line is a LOESS curve to guide the eye. See the text for details. In Figure 9 we present a final and more complex consistency test. Here, we analyze the influence of every observational point in the regression coefficients. This influence is calculated using the Cook's distance (Sheather 2009 , D i ). This distance is calculated as a combination of the residual and the leverage (or how isolated a value is) for every point. The plots of Figure 9 show the standardized residuals as a function of the leverage, and the Cook's distance is represented by the size of the points. According to Weisberg ( 2005 ), “... if the largest value of D i is substantially less than one, deletion of a case will not change the estimate ... by much.”