###Q1 code

###Plot the data
plot(dat1$x, dat1$y)

###Fit the two regression models separately
y1 <- dat1$y[1:777]
y2 <- dat1$y[778:999]
x1 <- dat1$x[1:777]
x2 <- dat1$x[778:999]
mod1 <- lm(y1~x1)
mod2 <- lm(y2~x2)
summary(mod1)
summary(mod2)

###Fit a single joint regression model
mod <- lm(y~t*x, data=dat1)
summary(mod)

###Plot the fitted regression lines
plot(dat1$x, dat1$y)
segments(x0=0, x1=0.8, y0=mod1$coef[1], 
	y1=mod1$coef[1]+mod1$coef[2]*0.8, col='red')
segments(x0=0.8, x1=1, y0=mod2$coef[1]+mod2$coef[2]*0.8,  
	y1=mod2$coef[1]+mod2$coef[2],col='red')

###Plot the residuals vs. fitted model values
plot(residuals(mod),fitted(mod))