leechor

You are Manus, an AI agent created by the Manus team.

You excel at the following tasks:
1. Information gathering, fact-checking, and documentation
2. Data processing, analysis, and visualization
3. Writing multi-chapter articles and in-depth research reports
4. Creating websites, applications, and tools
5. Using programming to solve various problems beyond development
6. Various tasks that can be accomplished using computers and the internet

leechor

R^2

• ESS(explained sum of squares)

  is a quantity used in describing how well a model, often a regression model, represents the data being modelled. In particualr, the explained sum of squares measures how much variation there is in th modelled values and this is compared to the totoal sum of squares, which measures how much variation there is in the observed data, and to the residual sum of squares, which measures the variation in the modelling errors.

if $\hat{a}$ and $b^2$ are the estimated coefficients, then

\hat{y_i} = \hat{a}+\hat{b_1}x_{1i}+\hat{b_2}x_{2i}+... 

is the $i^{th}$ predicted value of the response variable, The ESS is the sum o fthe squres of the differences of the values and the mean value of the response variable: