# Derive the expression for $\operatorname{Var}(b_1)$ for the no-intercept linear model y = $b_1$*$x_i$ + $ε_i$

Note: $$b_1$$ is the estimate for $$β_1$$

What I tried:

$$\operatorname{var}(b_1) = \operatorname{var}( Σ(x_iy_i)/Σx_i^2)$$

$$\operatorname{var}(b_1)= (1/(Σx_i^2)^2) * Σx_i * \operatorname{var}(y_i)$$

Since $$\operatorname{var}(y_i) = σ^2$$

$$\operatorname{var}(b_1) = σ^2/Σx_i^2$$

Is this correct?