Q:

What is a regression coefficient?

A:

A regression coefficient, commonly represented by an "m," is the slope of a straight line. This slope is obtained by fitting a linear equation to a data set containing two variables, typically "x" and "y."

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The regression coefficient can be derived from a data set using the least squares method. Least squares fits a line to a set of points by minimizing the sum of the squared distances of the points from the line, yielding the linear equation mx + b. In this equation, m is the regression coefficient and b is the point at which the line intersects the y-axis, called the intercept.

The value of the regression coefficient contains information about the relationship between the variables x and y. When m is large, y tends to increase more rapidly than x. The reverse is also true. When m is small, y tends to increase more slowly than x. However, the value of m gives no information as to the strength of the relationship between x and y, or the correlation. A highly correlated data set, when plotted, forms a tightly clustered line shape. A data set with low correlation is closer to elliptical or round in shape and may have no discernible shape at all.

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