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if the sum of squared differences of each sbp value from the regression line is smaller than the total sum of squares, then the regression line (serum cholesterol) has a better fit to the data than the mean sbp. the better the fit of the regression line the smaller the residual sum of squares( graph C).
$\begingroup$ Would like to add that in many texts, SSE is used to denote explained sum of squares (your SSreg and SS(Regression)). Those texts use SSR for residual sum of squares (your SSE and SS(Residual)). $\endgroup$ –
Clarifying the distribution of residual sum of squares for a linear regression. 1.
That is the amount of sum of squares that could reduced from the total sum of squares "attributable to having fitted the regression". $\endgroup$ – User1865345 Commented Jul 5, 2023 at 14:39
In addition to the points made by Peter Flom and Lucas, a reason for minimizing the sum of squared residuals is the Gauss-Markov Theorem. This says that if the assumptions of classical linear regression are met, then the ordinary least squares estimator is more efficient than any other linear unbiased estimator.
Deriving Regression Sum of Squares (SSR) Ask Question Asked 10 years, 4 months ago.
In linear regression, this is no different. We fit the line such that the sum of all differences between our fitted values (which are on the regression line) and the actual values that are above the line is exactly equal to the sum of all differences between the regression line and all values below the line. Again, there is no inherent reason ...
Edit: I am talking about sum of squares due to regression which is defined as $\sum (\hat{y}_i-\bar{y})^2$ this has degrees of freedom p-1 where p is the number of parameters in the model. SST which is defined as $\sum (y_i-\bar{y})^2$ has degrees of freedom n-1 and SSE (sum of squares due to error/residuals) is defined as $\sum (\hat{y}_i-y_i ...
Residual sum of squares in a regression. Hot Network Questions In a (math) PhD personal statement ...
I consider the following linear model: ${y} = X \beta + \epsilon$. The vector of residuals is estimated by ...