By Michael J. Campbell
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Additional info for Statistics at Square Two: Understanding Modern Statistical Applications in Medicine
Example text
If the model were correct one would expect to see the scatter of residuals evenly spread about the horizontal axis and not showing any pattern. e. the scatter gets larger as the x variable gets larger. This is often also associated with nonlinearity as well, and so attempts at transforming the x variable may resolve the issue. The final assumption is that the error term is Normally distributed. One could check this by plotting a histogram of the residuals, although the method of fitting will mean that the observed residuals ei are likely to be closer to a Normal distribution than the true ones i.
Iii) The relationship between mortality and median income is assumed to be different for the USA and Canada. (iv) The relationship between mortality and median share of income is assumed linear. (v) The variability of the residuals is assumed the same for the USA and Canada. 2. In a multiple regression equation yϭaϩb1X1ϩb2X2, (i) The independent variables X1 and X2 must be continuous 35 STATISTICS AT SQUARE TWO (ii) The leverage depends on the values of y. (iii) The slope b2 is unaffected by values of X1.
13. 14. 15. 8 Stepwise regression When one has a large number of independent variables, a natural question to ask is, what is the best combination of these variables to predict the y variable? To answer this one may use stepwise regression which is available in a number of packages. Step-down or backwards regression starts by fitting all available variables and then discarding sequentially those that are not significant. Step-up or forwards regression starts by fitting an overall mean, and then selecting variables to add to the model according to their significance.



