# A goal here is to build a multiple regression model to predict PSA level PSA from a subset of the predictors:
# the cancer volume, Prostate weight, Age, Benign prostatic and Capsular penetration.

# (1) Looking at the data. Plot scatter plot matrix, correlation matrix of Y and a subset of predictors, and briefly comment on them.

psa <- read.table(fn.data, header=TRUE)

# remove the variables we don't want to use for this assignment
psa <- subset(psa, select = names(psa)[-c(1,7,9)])
names(psa)

# simplify column names
colnames(psa)

# i. Looking at the dataset
# From the below summaries it is observed that there are 97 obs. and 6 variables in total out of which one is the response variable(PSA) and rest of the 5 variables are predictors (cancer_volume, prostate_weight, patient_age, benign_prostatic_hyperplasia, capsular_penetration). From the summary of benign_prostatic_hyperplasia it is observed that around 25% (1st Qartile) is 0 similarly for capsular_penetration variable. Also it is observed that there is no missing value in the data

dim(psa)

head(psa, 5)

summary(psa)

# Below is the scatterplot and correlation matrix of Y and predictors. By observing the scatterplot and correlation matrix, it seems PSA has the strongest linear relationship (0.624) with cancer_volume. Other variable with moderate correlation is capsular_penetration (0.55), whereas prostate_weight, patient_age, benign_prostatic_hyperplasia have low or no linear relationship with PSA.

# Scatter plots
pairs(~PSA+cancer_volume+prostate_weight+patient_age+benign_prostatic_hyperplasia+capsular_penetration, data = psa)

# Correlation Matrix
cor(psa)

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