Adding and Subtracting Vectors Using Components. Another common extension of the box model is the 'box-and-whisker' plot, which adds vertical lines extending from the top and bottom of the plot to, for example, the maximum and minimum values. A common version is to place a horizontal line at the median, dividing the box into two. The box lies on a vertical axis in the range of the sample. A multitude of statistics are available to summarize and test data. When we explore relationships between multiple variables, even more statistics arise, such as the coefficient estimates in a regression model or the Cochran-Maentel-Haenszel test statistic in partial contingency tables. Recognize whether a function has an inverse by using the horizontal line test. The Existence of Inverse Functions and the Horizontal Line Test. This graph shows the various scattered data points of test scores. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation. Here is a scatter plot that shows a correlation between ordinary test scores and final exam test scores for a statistics class:. Therefore, this best fit line is called the least squares regression line. Any other potential line would have a higher SSE than the best fit line. Drawing vertical strips on top of a scatter plot will result in the $y$-values included in this strip forming a new data set. Similarly, in testing for differences between sub-populations using a location test, some standard tests assume that variances within groups are equal. 
When a scatter plot is heteroscedastic, the prediction errors differ as we go along the regression line.Another way of putting this is that the prediction errors will be similar along the regression line.Imagine that you have a scatter plot, on top of which you draw a narrow vertical strip.This is called the vertical line test of a function.This mapping or set of ordered pairs is a function because the points do not make a vertical line.If an $x$value were to repeat there would be two points making a graph of a vertical line, which would NOT be a function.We can also tell this mapping, and set of ordered pairs is a function based on the graph of the ordered pairs because the points do not make a vertical line.Any vertical line in the bottom graph passes through only once and hence passes the vertical line test, and thus represents a function.
Thus, it fails the vertical line test and does not represent a function.The vertical line test demonstrates that a circle is not a function.Apply the vertical line test to determine which graphs represent functions.The vertical line test is used to determine whether a curve on an $xy$-plane is a function.Examples of vertical line test in the following topics:
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