To solve this, we need to compute $s^2$, which is the estimator of the variance $\sigma^2$ of the random error term $\epsilon$. The formula for $s^2$ when using a least squares fit is:

$s^2 = \frac{SSE}{n - 2}$

Where:

• $SSE$ is the sum of squared errors, which is given as 0.766.
• $n$ is the number of data points, which is 26.

So, let's compute $s^2$:

$s^2 = \frac{0.766}{26 - 2}$

I will calculate this for you.The value of $s^2$, the estimator of $\sigma^2$, is approximately 0.0319 when rounded to four decimal places.

Would you like to proceed with part (b), which asks for the estimate of $\sigma$, or clarify any details?

Here are 5 questions to deepen your understanding:

1. How is the sum of squared errors (SSE) computed in a least squares regression?
2. Why do we divide by $n - 2$ instead of $n$ when estimating $s^2$?
3. How does increasing the number of data points affect the value of $s^2$?
4. Can $s^2$ be used to directly estimate the standard error of the regression?
5. What are the assumptions about errors when performing least squares fitting?

Tip: The variance $\sigma^2$ describes the spread of the random error term, while $\sigma$ (its square root) represents the standard deviation of these errors.