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Oct 27, 2019 · The F-test, when used for regression analysis, lets you compare two competing regression models in their ability to “explain” the variance in the dependent variable. Linear Regression: SST, SSR, SSE, R-squared and Standard Error with Excel ANOVA Подробнее. Proof that total sum of squares = explained sum of squares plus the sum of squared residuals Подробнее.

My motivation for asking this question is that people often say that an R squared value isnt appropriate for a non-linear model because SSt=SSe + SSr does not hold. I apologize for my ignorance in advance.
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Title: class6 Author: ingo Created Date: 3/8/2010 2:12:20 AM
The sum of squares is a tool statisticians and scientists use to evaluate the overall variance of a data set from its mean. A large sum of squares denotes a large variance, which means that individual readings fluctuate widely from the mean.
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For SSE use the below formaula: SST = SSE+SSR I have a detailed answer explaining the above concept you may go on...
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  • Σ(YY$− )2 is the sum of squares due to the linear regression SSR, with mean square MSR. Σ(YY− $)2 is the sum of squares not explainable by the regression line, and is called the residual sum of squares Ssr, with mean square Msr. This information can be summarized in an analysis of variance table (Table 10-3). Table 10-3.
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  • I wish to differ here. There is a correlation R^2 and the slope when we take into consideration the sum of square total(SST), the proof can be deduced this way : SST = SSR + SSE Diving through by SST.
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= SSR SST. • It represents the portion of total variation in y-values attributable to difference in values of independent variables or covariates. Correlation between Y and X1. This has been verified numerically & I found a proof in a book on "Linear Models" by Ronald Christensen.
The first term on the right, SSE/SST, measures SSE as a proportion of SST, or the proportion of the variation in \(Y\) accounted for by the fitted valued. From this equation, we define \[ R^2 = 1 - \frac{SSR}{SST} \] as a measure of the goodness-of-fit of the regression. By construction, the \(R^2\) lies between zero and one. If the model fits ...

What exactly is SSE, SSR and SST? What is the difference between a POPULATION regression function and a SAMPLE regression line? Why are there so many different types of error terms??

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Proof that E(RSS) = (n−2)σ2 Recall from the notes that the residual sum of squares, RSS, can be written as: S yy − S2 xy S xx and that βˆ = S xy S xx Now note that these can be put together to give RSS = S yy − S 2 xy S xx = S yy − S xy S2 xx! S xx = S yy −βˆ2S xx The expectation of this can therefore be found by finding in turn ...