To answer this question, we need to have access to the actual data of the FatMice18 dataset, in particular, the variable 'WgtGain4'. However, regardless of having the data, we can explain the process of how one can derive the sum of squares for the NULL or empty model of 'WgtGain4'.
1. The NULL or empty model refers to a model with no predictors or independent variables. In such a case, we only include an intercept which is the mean of 'WgtGain4'.
2. To fit the NULL model, we simply calculate the mean of 'WgtGain4'. The mean is the sum of all the values in 'WgtGain4' divided by the number of observations.
3. Once we have the mean, the next step is to calculate the sum of squares for the NULL model. The sum of squares is a measure of the total variation within a dataset.
4. To calculate the sum of squares, we subtract the mean of 'WgtGain4' from each individual observation in 'WgtGain4', square the result of each subtraction, and then sum up all these squared values.
5. The resulting value is the sum of squares for the NULL model. This value signifies how much of the variation in the data the model does not explain. Since the NULL model has no predictors, this sum of squares would equate to the total variability in 'WgtGain4'.
Without the actual data, it is not possible to compute the sum of squares for the NULL model of 'WgtGain4', and thus we cannot directly answer the multiple choice question. The examples (A, B, C or D) provided in the question are purely hypothetical. The actual sum of squares would be computed following the above steps provided the data of FatMice18 is available.