Problem
Scientists are interested in predicting the cancer volume (in mm3) from a blood marker measurement for patients who are known to have prostate cancer. The file prostate.csv contain the blood marker measurement and cancer volume for 200 prostate cancer pa- tients.
1. Identify the independent and dependent variable in this experiment.
2. Load the dataset into Python and create an appropriate graphical summary of the data. Describe the plot.
3. Compute the correlation coefficient between the cancer volume and the blood marker measurement. Does this indicate a strong or weak linear relationship? Is the rela- tionship positive or negative?
4. Fit a linear regression model to the data. Describe the fitted relationship.
5. A new prostate cancer patient arrive at the clinic with a blood marker measurement of 4.3 mm3. Use the fitted model to predict the cancer volume for this patient.
6. Examine the model residuals to determine if the assumptions about the random component of the linear regression model are met.
7. After reviewing the data, the scientists realise that their equipment is inaccurate for blood marker measurements below 1. As such, patients with a blood marker measurement of less than 1 must be removed from the analysis. Remove these patients from the dataset and redo your analysis. Does this improve the model fit? Explain your reasoning.