Regression is about finding the ‘line of best fit’ for some data. R-Squared is a way of measuring wether the line of best fit describes the data well.
Imagine your data points on a graph, and you have a stright line at random going through the points. Then imagine you fastened elastic bands on each of the points and the line. They would pull the line into the ‘line of best fit’. This is essentially regression, as the elastic bands pull and get shorter, the line moves and twists, and on average gets closer to all the points. The length of the elastic bands is also called the error.
R squared is a measure of how close the line is to the points, or how low the overall error is, or how short your elastic bands are. If the points are all in a straight line then the length of your elastic is small. If the points are not correlated, if they’re all over the place, then the elastic is going to be stretched and taught, meaning a high error and a low R squared
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