Let's continue with the previous example of scatter plot and extend this to a bivariate regression. Let's discuss missing data bias and error problems for the three missingness mechanisms (Nakagawa and Freckleton, 2008).

- In MCAR, the slope is unbiased and the expected R2 is the same as for the original data.
- In MAR, the expected slope is unbiased as missingness depends on X, with the result that covariance between X and Y is reduced by the same amount as the reduction in standard deviation of X. However, the R2 would be reduced.
- In MNAR, the slope is biased as missingness is determined by Y and R2 is reduced.

## Question

It is often impossible in practice to determine whether data are MNAR, because doing so would require comparing observed Y values to missing Y values, and you do not have access to the missing Y values.

1. True
2. False

The answer is True. The point of delineating the three missing data mechanisms is not to determine which missing data mechanism is at work in a particular data set. Instead, the point of describing MCAR, MAR, and MNAR mechanisms is to illustrate the assumptions underlying different missing data treatments. For example, CCA is unbiased under MCAR.