equation for least squares regression line calculator

The following illustration shows the order in which the additional regression statistics are returned. For information about how ssreg and ssresid are calculated, see 'Remarks,' later in this topic. For information about how df is calculated, see 'Remarks,' later in this topic. Compare the values you find in the table to the F statistic returned by LINEST to determine a confidence level for the model. Use the degrees of freedom to help you find F-critical values in a statistical table. Use the F statistic to determine whether the observed relationship between the dependent and independent variables occurs by chance. The F statistic, or the F-observed value. For information about how r 2 is calculated, see 'Remarks,' later in this topic. At the other extreme, if the coefficient of determination is 0, the regression equation is not helpful in predicting a y-value. If it is 1, there is a perfect correlation in the sample - there is no difference between the estimated y-value and the actual y-value. Compares estimated and actual y-values, and ranges in value from 0 to 1. The standard error value for the constant b (seb = #N/A when const is FALSE). The standard error values for the coefficients m1,m2.,mn. The additional regression statistics are as follows. If stats is FALSE or omitted, LINEST returns only the m-coefficients and the constant b.

The array that the LINEST function returns is.

The m-values are coefficients corresponding to each x-value, and b is a constant value. If there are multiple ranges of x-values, where the dependent y-values are a function of the independent x-values. Instructions follow the examples in this article. Because this function returns an array of values, it must be entered as an array formula. You can also combine LINEST with other functions to calculate the statistics for other types of models that are linear in the unknown parameters, including polynomial, logarithmic, exponential, and power series. The LINEST function calculates the statistics for a line by using the 'least squares' method to calculate a straight line that best fits your data, and then returns an array that describes the line. Find links to more information about charting and performing a regression analysis in the See Also section. This article describes the formula syntax and usage of the LINEST function in Microsoft Excel.

Equation for least squares regression line calculator