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Does an influential point affect correlation?
Outliers and high-leverage points can be influential to different measurements in least-squares regression like the slope, y-intercept, and correlation coefficient (r).
Does removing an outlier increase or decrease correlation?
Influence Outliers Influential outliers are points in a data set that influence the regression equation and improve correlation. But when this outlier is removed, the correlation drops to 0.032 from the square root of 0.1%.
Does correlation increase when outliers are removed?
When the outlier in the x direction is removed, r decreases because an outlier that normally falls near the regression line would increase the size of the correlation coefficient.
What happens when nonconstant variance is too high?
For example, if the residual variance increases with the fitted values, then prediction intervals will tend to be wider than they should be at low fitted values and narrower than they should be at high fitted values. Some remedies for refining a model exhibiting excessive nonconstant variance includes the following:
How to account for non-constant variation across the data?
Transform the response variable to equalize the variation across the levels of the predictor variables. Transform the predictor variables, if necessary, to attain or restore a simple functional form for the regression function. Fit and validate the model in the transformed variables.
When to use weighted least squares for nonconstant variance?
A plot of the residuals versus the predictor values indicates possible nonconstant variance since there is a very slight “megaphone” pattern: We will turn to weighted least squares to address this possiblity. The weights we will use will be based on regressing the absolute residuals versus the predictor.
How can we detect non-constant variance in real life?
There was no constant standard deviation when we created the “noise”. Each random value was drawn from a different Normal distribution, each with mean 0 but a standard deviation that varied according to x. This means our assumption of constant variance is violated. How would we detect this in real life?