bolly <- read.csv("http://www.stat.ufl.edu/~winner/data/bollywood_boxoffice.csv")
attach(bolly); names(bolly)


## Plot (G vs B), (logG vs B), (G vs logB), (logG vs logB)
## Goal: Linear (straight line) relation with 
##      approx constant spread around line

par(mfrow=c(2,2))     ## Plot 4 plots on 1 screen (2 r0ws, 2 cols)
plot(Gross ~ Budget, main="Y=Gross, X=Budget")
abline(lm(Gross~Budget))
plot(log(Gross) ~ Budget, main="Y=log(Gross), X=Budget")
abline(lm(log(Gross) ~ Budget))
plot(Gross ~ log(Budget), main="Y=Gross, X=log(Budget)")
abline(lm(Gross ~ log(Budget)))
plot(log(Gross) ~ log(Budget), main="Y=log(Gross), X=log(Budget)")
abline(lm(log(Gross) ~ log(Budget)))

## Define Y=log(Gross) and X=log(Budget)
Y <- log(Gross)
X <- log(Budget)

## Q.3. Fit regression and obtain summary and save fitted values and resids

bolly.reg <- lm(Y ~ X)
summary(bolly.reg)
yhat <- predict(bolly.reg)
e <- resid(bolly.reg)

## Q.4. Obtain fitted value for "Race 2" which is the 54th film in the dataset
## Print side-by-side using "cbind": yhat_54, e_54, exp(yhat_54)

cbind(yhat[54], e[54], exp(yhat[54]))

## Q.5. Correlation for: raw data, log data, spearman's rank correlation
##    Spearman's Correlation obtains correlation of ranks, less effected
##    by outlying observations

cor(Budget, Gross) 
cor(Y, X)
cor(Budget, Gross, method="spearman"); cor(Y, X, method="spearman")

## Q.6. Computed "manually" by definitions (SSR and SSE also obtained 
           from anova function), see Q.10.

(TSS <- sum((Y - mean(Y))^2))     ## sum(y - ybar)^2
(SSR <- sum((yhat - mean(Y))^2))  ## sum(yhat - ybar)^2
(SSE <- sum((Y - yhat)^2))        ## equivalent to sum(e^2)       

## Q.7. Computed "manually", but also see summary from Q.3.

(rsq1 <- SSR/TSS)
(rsq2 <- 1 - (SSE/TSS))

## Q.8. see summary from Q.3.

## Q.9. be sure to select correct parameter 

confint(bolly.reg)

Q.10. Note:  R doesn't print the "Total" line

anova(bolly.reg)