Mathematically, the error of the i th point on the x-axis is given by the equation: (Y i – Ŷ i), which is the difference between the true value of Y (Y i) and the value predicted by the linear model (Ŷ i) - this difference determines the length of the gray vertical lines in the plots above. In the plots above, the gray vertical lines represent the error terms - the difference between the model and the true value of Y. Therefore, using a linear regression model to approximate the true values of these points will yield smaller errors than “example 1”. This is because in “example 2” the points are closer to the regression line. Just by looking at these plots we can say that the linear regression model in “example 2” fits the data better than that of “example 1”. Plotted below are examples of 2 of these regression lines modeling 2 different datasets: (The other measure to assess this goodness of fit is R 2).īut before we discuss the residual standard deviation, let’s try to assess the goodness of fit graphically.Ĭonsider the following linear regression model: The residual standard deviation (or residual standard error) is a measure used to assess how well a linear regression model fits the data.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |