of Kvålseth is used, R2 can be greater than one. In all instances where R2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SSres. In this case, R2 increases as the number of variables in the model is increased (R2 is monotone increasing with the number of variables included—it will never decrease). This illustrates a drawback to one possible use of R2, where one might keep adding variables (kitchen sink regression) to increase the R2 value. For example, if one is trying to predict the sales of a model of car from the car's gas mileage, price, and engine power, one can include such irrelevant factors as the first letter of the model's name or the height of the lead engineer designing the car because the R2 will never decrease as variables are added and will likely experience an increase due to chance alone. This leads to the alternative approach of looking at the adjusted R2. The explanation of this statistic is almost the same as R2 but it penalizes the statistic as extra variables are included in the model. For cases other than fitting by ordinary least squares, the R2 statistic can be calculated as above and may still be a useful measure. If fitting is by weighted least squares or generalized least squares, alternative versions of R2 can be calculated appropriate to those statistical frameworks, while the "raw" R2 may still be useful if it is more easily interpreted. Values for R2 can be calculated for any type of predictive model, which need not have a statistical basis. In a multiple linear model Consider a linear model with more than a single explanatory variable, of the form where, for the ith case, is the response variable, are p regressors, and is a mean zero error term. The quantities are unknown coefficients, whose values are estimated by least squares. The coefficient of determination R2 is a measure of the global fit of the model. Specifically, R2 is an element of [0, 1] and represents the proportion of variability in Yi that may be attributed to some linear combination of the regressors (explanatory variables) in X. R2 is often interpreted as the proportion of response variation "explained" by the regressors in the model. Thus, R2 = 1 indicates that the fitted model explains all variability in , while R2 = 0 indicates no 'linear'