That equation is called the least squares regression equation.īut how do we measure best? The criterion is called the least squares criterion and it looks like this: Any other equation would not fit as well and would predict Y with more error. In other words, there exists one formula that will produce the best, or most accurate predictions for Y given X. It turns out that with any two variables X and Y, there is one equation that produces the "best fit" linking X to Y. If X is 10, then the formula produces a predicted value for Y of 45 (from 10 + 5*7). Such a formula could be used to generate values of for a given value of X. ![]() ![]() The regression line takes the form: = a + b*X, where a and b are both constants, (pronounced y-hat) is the predicted value of Y and X is a specific value of the independent variable. Regression generates what is called the "least-squares" regression line.
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