Q1) (a) It seems reasonable that the size of a cancerous tumor should be related to the likelihood that the cancer will spread (metastasize) to another site. The article Molecular Detection of p16 Promoter Methylation in the Serum of Patients with Esophageal Squamous Cell Carcinoma (Cancer Res. 2001: 3135-3138) investi- gated the spread of esophageal cancer to the lymph nodes. With x = size of a tumor (cm) and Y 1 if the cancer does spread, consider the logistic regression model with = 0.5 and 0 = -2 (values suggested by data in the article). Then = = -2+0.52 e p(x) = 1+e-2+0.5x (i) Compute odds when x = 6.77 and interpret the result. (ii) Interpret the value of the slope . (b) Let (x1,y1), (X2, Y2), , (xn, Yn) be the observed n-pairs. The response variable Yi (i = 1, 2. ,n) is a binary variable which takes the value either 1 (success) or 0 (failure). The probability of success for given x is defined by ... p(x) = eBo+B1x 1+eo+1x * Find the likelihood function.