This breast cancer database was obtained from the University of Wisconsin Hospit
ID: 3234134 • Letter: T
Question
This breast cancer database was obtained from the University of Wisconsin Hospitals, Madison. 699 samples were collected, each of which is diagnosed of developing breast cancer or not. Features are computed from an image of a fine needle aspirate (FNA) of a breast mass. They describe characteristics of the cell nuclei present in the image, including clump thickness, uniformity of cell size, uniformity of cell shape, marginal adhesion, and single epithelial cell size. All features were measured in a scale of 1 10. The R output is shown for a logistic regression model of the sample status (cancer or not) versus these features. Null deviance: 900.53 on 698 degrees of freedom Residual deviance: 167.03 on 693 degrees of freedom AIC: 179.03 (a) We observe that all values in the "Estimate" column are positive (except the intercept). What does this observation imply in terms of how these features affect the risk of developing cancer? (b) What is the odds ratio of developing breast cancer, when the epithelial cell size increases by 1 unit? What if the epithelial cell size increases by 3 units?Explanation / Answer
a)
This means that increase in either of the variables would lead to rise in risk of developing cancer. For example, one unit increaes in uniformity of cell size would lead to increase of 0.2252 in the risk of developing cancer, all other factors remaining constant. All other variables would lead to increase in risk of developing cancer by their respective coefficients.
b)
0.2917 if increase by 1 unit and 0.8751 if increase by 3 units.
c)
The confidence interval for epithelial cell size is estimate+-z-value*std error
0.2917+-1.96*0.1356=0.02546 0.55794