4. Sometimes we can transform data that are not symmetric and bell-shaped to more closely resemble a Gaussian distribution. The data below give observed values (y) for the survival times (in months) after treatment for a certain type of cancer. There are a total of 72 observations. f. Now "undo" the transformation for the model-based quantiles from part e. to 10 15 5 19 18 76 17 18 11 16 5 18 get the corresponding theoretical quantiles for the original survival data. Compare these theoretical values with the sample quantile values by organizing the results in a table (like 94 8 42 4 9 7 12 50 7 42 16 2 the one given below). Please give results to 3 decimal places, where appropriate. Note: If a quantile value is 5, just write 5, or if it's 3.75, just write 3.75. Otherwise, express to 3 d.p 44 36 4 22 17 8 7 38 19 22 10 14 950 967 995 12 4 5 12 13 7 11 5 24 23 6 21 Theoretical Quantiles (exa) 13 9 4 9 14 23 10 17 64 9 18 25 Sample Quantiles (ya) 6 16 10 7 7 8 10 8 11 46 11 22 C. Now, consider a new variable, call it y", where y" = log.(y) (which is the same as In(y)). R uses the command log for In, by default. Plot a histogram for y* and comment on Note: To find the sample quantiles, you do not need to sort the data. Please use the R its shape. function quantile to determine the sample quantiles of the original survival data. d. For the transformed data, calculate the sample mean, sample standard Comparing the values in the table, answer the following: deviation, sample skewness, and sample kurtosis for the survival data. Based on the How closely do these model-based quantiles compare to the sample quantiles from the skewness and kurtosis values for the transformed data, does a Gaussian model seem more original data? Based on these findings, and other findings from this question, comment on appropriate? Comment / explain. the model fit. e. Assuming that the transformed data follow a Gaussian distribution, with a mean of y*and a standard deviation of s', find the 0.5, 0.67, and 0.95 quantiles of the transformed data. Hint: The a-quantile of a G(u, o) distribution is given by: Xa = U + ZaO where za is the a-quantile of the standard Normal distribution