How do I calculate the standard error of beta-1 in a regression model?

Question

I missed class during this day because of the flu (yes it was real and documented :-) ). Now I am having trouble finding out how to calculate some of the material we covered. That said, any help would be useful. Thanks.

Answer 1

Compute the residuals e(i) from the regression equation .as follows:

e(i)= y(i)-a-bx(i)

where b is the regression coefficient and a is the y-intercept.

Compute the standard deviation of the residuals S(e)



Standard error of b= S(e) / SQRT [Σ (x(i)-xbar)^2]



where xbar is the mean of x's

Answer 2

Standard Error Of Beta

Answer 3

you're able to use diverse regression information once you're surprisingly helpful that a sequence of records is a function of better than one variable, or could be extra perfect represented by way of a polynomial than by way of different applications. working example, the value of possessing an motor vehicle could be represented as a function of preliminary value, time, distance traveled, hours of engine working time, and style of engine starts. Regressing on each and each if those variables independently won't provide you a real photograph of othe value dependency, yet a undeniable linear regression will yield a clearer photograph. you are able to postulate that F = a + bw + cx + dy + ez the place F = working entire of money spent a = preliminary value (inclusive of "hidden" preliminary fees of different variables) w = mileage x = time of possession y = engine hours (from an hour meter), and z = engine starts (from a counter on the ignition) You build your database, of direction, by way of recording each and all of the variables each and every time you have an expenditure, alongside with the expenditure. answer of the regression is as follows: | n.. ?w... ?x... ?y... ?z.. . | |a| |?F| |?w ?w^2 ?wx. ?wy. ?wz.. | |b| |?wF| |?x. ?wx.. ?x^2 ?xy.. ?xz.. | |c| |?xF| |?y. ?wy. ?xy.. ?y^2 ?yz.. | |d| |?yF| |?z. ?wz.. ?xz.. ?yz.. ?z^2 | |e| |?eF| This instruments up somewhat on a spreadsheet for answer by way of removing. so some distance, i've got not arise with an analog for the correlation ingredient, so I upload columns to the spreadsheet to income envisioned values to truly values, and take the many times taking place deviation of the blunders as a sort of diploma of in wonderful condition. Graphing and visualizations are stressful again by way of. edit: Sorry, the SPSS did not sign in till once I typed each and all of the above drivel.

Answer 4

Remember to divide SSE by n-2 when computing s^2.