Code time about the middle year $1936$ so $u=\text{year}-1936$. With $n=11$, $\sum y=33$, $\sum u=0$, $\sum u^{2}=110$, $\sum uy=44$, the least-squares line $\hat y=a+bu$ has $a=\dfrac{\sum y}{n}=3$ and $b=\dfrac{\sum uy}{\sum u^{2}}=0.4$, giving $\hat{y}=3+0.4u$.

Coding the time. There are $11$ years ($1931$ to $1941$), an odd count, so we shift the origin to the middle year $1936$ and let

$u=\text{year}-1936,$

which makes $\sum u=0$ and simplifies the normal equations.

Preparing the totals.

Normal equations. For the line $\hat y=a+bu$ the least-squares normal equations are …