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It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. [8] Functions with multiple outputs are often referred to as vector-valued functions.
The above equations are efficient to use if the mean of the x and y variables (¯ ¯) are known. If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the α ^ and β ^ {\displaystyle {\widehat {\alpha }}{\text{ and }}{\widehat {\beta }}} equations.
That is, one may consider y as a dependent variable (output) obtained from the independent variable (input) x via a linear function: = = +. In the xy-coordinate plane, the possible values of (,) form a line, the graph of the function ().
In the formula above we consider n observations of one dependent variable and p independent variables. Thus, Y i is the i th observation of the dependent variable, X ij is i th observation of the j th independent variable, j = 1, 2, ..., p. The values β j represent parameters to be estimated, and ε i is the i th independent identically ...
Regression models predict a value of the Y variable given known values of the X variables. Prediction within the range of values in the dataset used for model-fitting is known informally as interpolation. Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions.
For two continuous variables, a scatterplot is a common graph. When one variable is categorical and the other continuous, a box plot is common and when both are categorical a mosaic plot is common. These graphs are part of descriptive statistics .
The first 12-team College Football Playoff field was revealed on Sunday. Undefeated Oregon earned the top seed, while SMU beat out Alabama for the 12th and final spot. Oregon, Georgia, Boise State ...
A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, [2] is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed.