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Essentially, garbage in, garbage out. This indicates that the values are too small negative or too large positive compared to what we would expect for a normal distribution. So for the sample size ofwe would conclude that that normality assumption is violated.
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Equal Variance: the error variance is the same at any set of predictor values. The most obvious would be to make a histogram of the residuals. The distributions of the parameter estimates will not be what we expect.
movel If all we would like to do is predict, possibly not, since we would only care about the size of our errors. This matches our findings with a fitted versus residuals plot.
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We see with the large sample size, all of the points are rather close to the line. If these assumptions are met, great! It could be that the errors are made in a systematic way, which means that our model is misspecified. It will be useful for checking both the linearity and constant variance assumptions.
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The errors have non-constant variance about the true model. At every fitted value, the spread of the residuals should be roughly the same. This is bad! To get a better idea of how a fitted versus residuals plot can be useful, we will simulate from models with violated assumptions. Next, we simulate data from an exponential distribution.
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While a fitted versus residuals plot can give us an idea about homoscedasticity, sometimes we would prefer a more formal celebrity escort. However, they are not even ofr to centered at zero! We can perform inference, and it is valid.
This would suggest that the errors do not follow a normal distribution. Be able to identify unusual observations in regression models. In R these are very easy to make. However is that all we care about?
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At any fitted value, the mean of the residuals should be roughly 0. If this is the case, the linearity assumption is valid. While many of the points are close to the line, at the edges, there are large discrepancies.
The Breusch-Pagan Test can not be performed by default in R, however the function bptest in the lmtest package implements the test. The constant variance assumption is violated here.
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At small and large fitted values the model is underestimating, while at medium fitted values, the model is overestimating. Hypothesis tests will then accept or reject incorrectly. For this reason we will usually use more powerful tools unnusual as Q-Q plots and the Shapiro-Wilk test for assessing the normality of errors.
If this is the case, the constant variance assumption is valid. There are many tests for constant variance, but here we will present one, the Breusch-Pagan Test. The errors have constant variance about the true model. However, if we would like to perform inference, for example to determine if a particular predictor is important, we care a great deal.
So the constant variance assumption escorts downtown halifax met, but the linearity assumption is violated.
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The linearity assumption is not violated. Notice in the first plot, one point is somewhat far from the line, but just one point, in combination with the small sample size, is not enough to make us worried. This is good! It is also possible that at a particular unusjal of predictor values, the errors are very small, but at a different set of predictor values, the errors are large.
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