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Regression - Chapter Six
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- 1The residual vector for a multivariate regression model is e_ = ? This then has variance given by Var(e_) = ? To find leverage points what do we look for? Usually values of hii > ? are considered as indicating points of high leveragee_ = y_ - y_hat
Var(e_) = (1-H)sigma^2
Large hii values
hii > 2(p+1)/n - 2Var(ei) = ? We can estimate sigma^2 as ? The studentised residuals are defined by ei* = ?Var(ei) = (1-hii)sigma^2
sigma^2hat = s^2 = RSS/n-p-1 = SIGMA(i=1,n)[yi - yihat]^2/n-p-1
ei* = ei/sqrt[s^2(1-hii)] - 3When we are plotting out residual points this is exactly the same as when doing it for a linear regression model however with a multivariate we do one thing extra what is this?We plot the studentised residuals against the fitted for values for each explanatory variable so there will be more than the one graph as with linear regression
- 4It is known that SIGMA(i=1,n)[hii] = ? So hiibar = ? Hence we use a cut off point ... to detect high leverage points To check the normality of a multivariate regression model we use?SIGMA(i=1,n)[hii] = (p+1)
hiibar = (p+1)/n
2(p+1)/n
qq-plots as with the linear regression model - 5To find influential points we use ... The formula for this is Di = ? What implies that there's an influential point? If we detect an influential point what can we do?Cook's distance as with linear regression
Di = [1/(p+1)]*[(ei)^2]*[hii/(1-hii)]
Large values of Di, well above most of the data
Remove this from the data and see if it has much of an effect on the variables
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- Fichas sobre Regression - Chapter Six, creado por Cara Wales el 26/05/2016.
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