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A tumor is an abnormal growth of cells that serves no purpose. A tumor can be benign, which is harmless, or malignant, which is cancer. A malignant tumor tends to be bigger compared to a benign tumor, as you've found in one of Week 7's problems.
The following is a simulated data containing 1000 observations of renal cortical tumors, a type of kidney tumors. The data can be downloaded here and then loaded to R using the command
tumor <- read.csv("tumor071.csv")
The first column, named 'size', is the tumor size in cm. The second column, named 'y', is an integer indicating whether the tumor is benign (y=0) or malignant (y=1).
Enter all of your answers in the following questions to 3 decimal places, unless stated otherwise.
a. Null model: what proportion of the tumors in the data set are malignant?
b. Fit a logistic regression model predicting the probability of a tumor being malignant from 'size'.
ln(odds) = + × size
c. How much do the estimated odds of the tumor being malignant change if the tumor increases in size by 1 cm? In other words what is the odds ratio for 'size'?
The rest of questions will show up after you finish (a)-(c).
