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Linear Estimation
The Linear Estimation study calculates and displays a Linear Regressive Slope and a Linear Regressive Intercept of the data given by the Input Data Input. The calculation is similar to the output of the basic LINEST function in Excel.
Let the Input Data at Index \(t\) be given as \(X_t\), and let the Length be given as \(n\). We denote the Linear Regressive Slope and Linear Regressive Intercept at Index \(t\) as \(b_t(X,n)\) and \(a_t(X,n)\), respectively, and we compute them as follows.
\(\displaystyle{b_t(X,n) = \frac{n \cdot \sum_{i=t-n+1}^t{(i-t+n)X_i} - \frac{n(n+1)}{2} \cdot \sum_{i=t-n+1}^t {X_i}}{n \cdot \frac{n(n+1)(2n+1)}{6} - \frac{n^2(n+1)^2}{4}}}\)\(\displaystyle{a_t(X,n) = \frac{\sum_{i=t-n+1}^t {X_i} - b_t(X,n) \cdot \frac{n(n+1)}{2}}{n}}\)
For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to our description here.
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*Last modified Monday, 09th January, 2023.