# Example: pi

radii = c(1.5, 3.5, 4.5, 5.0, 6.5, 10.0, 11.0)
?c

# Design matrix

X = cbind(rep(1,7), (4/3)*radii^3)
X



# Measurements, 7 experiments - one for each sphere
y = c(13.8, 181.6, 380.1, 521.7, 1149.6, 4195.4, 5574.3)



betahat = solve(t(X)%*%X)%*%t(X)%*%y
betahat




# predictions
yhat = X %*% betahat
yhat

# residuals
y-yhat


# next step...

x = (4/3)*radii^3
model = lm(y~x)
summary(model)