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In simple linear regression (which includes an intercept), r2 is simply the square of the sample correlation coefficient (r), between the observed outcomes and the observed predictor values The coefficient of determination is often written as r2, which is pronounced as “r squared.” for simple linear regressions, a lowercase r is usually used instead (r2). In simpler terms, it shows how well the data fit a regression line or curve R squared formula the coefficient of determination which is represented by r2 is determined using the following formula:
A value of 0 indicates that the response variable cannot be explained by the predictor. Therefore, the more points you add, the better the regression will seem to “fit” your data If your data doesn’t quite fit a line, it can be tempting to keep on adding data until you have a better fit Some of the points you add will be significant (fit the model) and others will not.
Here, too, it is easy to see that distances between the data points and the red line (our target model) will be larger than distances between data points and the blue line (the mean model). In summary, interpreting r 2 r2 involves understanding its scale (0 to 1 usually), relating the value to the percentage of variance explained, visualizing the fit, and most importantly, considering the context of the specific problem domain.
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