# estimate of a standard deviation for a linear model

A researcher wants to know how land size affects house value. He considers the following linear regression model,

$$y_i = \beta_0 + \beta_1 x_i + \varepsilon_i$$

where $y_i$ is the price of house $i$, measured in thousand dollars; $x_i$ is the land size, measured in square meters.

He collected 100 observations and obtained a point estimate $\hat \beta_1=5.2$ and an interval estimate $[5.0; 5.4]$ at 95% level.

Based on the information above, what is the value of the estimate of $\sigma_{\varepsilon}$ (the standard deviation of $\varepsilon$)?
Now, I know the answer is 1, and you can do that by finding the S$\beta_1$, but how do you find $SS_{xx}$? The solution manual says it's 100 but how do you find that out? The answer is 1.
• If that is a homework exercise, please add the self-study tag and read its Wiki. – Richard Hardy Oct 24 '15 at 8:49
• I think perhaps you've been taught that you should standardise your predictors (ie $\overline {x}=0, s^2_x=1$) before fitting the model? – probabilityislogic Oct 24 '15 at 10:38
Here's a hint: what is the formula for the 95% confidence interval? Do any terms in the formula for it look like an estimate of $\sigma_{\epsilon}$?