## typing in the data, the target y is the fraction of UK pupils admitted into Oxf/Cam
## the explanatory variable x is school_month
birth_month <- c(9:12,1:8)
school_month <- 0:11
number_admissions <- c(470,515,470,457,473,381,466,457,437,396,384,394)
number_pupils <- c(66776,64167,59603,62877,62543,57597,65319,62651,65454,64429,64612,62738)
y <- 100* number_admissions / number_pupils


## use pdf command to generate a pdf of the data plot; leave it and dev.off() away if you just want to generate a plot on the screen
pdf(file="admission.pdf",width=6,height=6)
plot(school_month, y, xlab="MONTHS AFTER SCHOOL YEAR STARTS",ylab="ADMISSION RATE INTO OXFORD/CAMBRIDGE (%)",pch=20,cex=2)
dev.off()

## fit a linear model with y as response variable and school_month as explanatory variable
linmod <- lm( y ~ school_month )

## generate a plot as before but add the regression line in red
pdf(file="admission_fit.pdf",width=6,height=6)
plot(school_month, y,xlab="MONTHS AFTER SCHOOL YEAR STARTS",ylab="ADMISSION RATE INTO OXFORD/CAMBRIDGE (%)",pch=20,cex=2)
lines(school_month, fitted(linmod),col="red",lwd=2)
dev.off()