yvalues

Y-values are the values of the dependent variable in a system that uses x-values as the independent variable. In a Cartesian plot, each data point is typically represented as (x_i, y_i), with x as the horizontal coordinate and y as the vertical coordinate. When a function y = f(x) is defined, the y-values are the outputs produced by applying the function to chosen x-values.

In statistics, y denotes the outcome or response variable, while x denotes a predictor or feature. In regression analysis, the goal is to model the relationship between x and y in order to predict y from x and to assess the strength and direction of that relationship. Y-values are central to various descriptive and inferential procedures, including the calculation of residuals, which are the differences between observed y-values and those predicted by a model.

In time series, y_t represents the value of the series at time t, and the sequence of y-values conveys the evolution of the measured quantity over time. In data handling, y-values may contain missing data, requiring imputation, exclusion, or modeling techniques that accommodate incomplete observations.

Common operations on y-values include computing summary statistics (mean, median, variance, standard deviation), identifying extremes (minimum and maximum), and examining their distribution via plots or histograms. When paired with corresponding x-values, y-values enable analyses of correlation and various forms of regression, as well as assessments of model fit through residual analysis.

Examples help illustrate the concept: if y = 2x + 1 and x takes values 0, 1, and 2, the resulting y-values are 1, 3, and 5.

In software and data workflows, y-values are stored as arrays, lists, or as a column in a dataframe, and are often plotted or modeled alongside their x-values.