# 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.

Answer the following question:
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 tried to introduce proper formatting for the formulas, but I could not figure out what Sb1 was in the last paragraph. Also, if you find other mistakes, you may either undo my edit (but then you would lose all the formatting) or try to fix it yourself, or make explicit what you mean in the last paragraph for me or someone else to format it for you. Also, you should come up with a more concrete and informative title, e.g. "Self-study: find error variance in regression". – Richard Hardy Oct 24 '15 at 8:58
• Please edit the title to something more informative. – JohnRos Oct 24 '15 at 9:35
• 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 $\sigma_{\epsilon}$?