Question

he haue a linar regrasion with the madel. Y=Bx+e (en N (0,6)) that passes through the origin- Meaning that E (Y1X) 0" You dispose of n (Xi,Mi), i = 1,...,n, of this model independent observation s %3D O What is the estimator 3 of the least Squores of B? What is the Sampling law o ß? (Pleaye carefully annote your Solution with a detail explanation Of everything that you do)

Answer 1

soin linear regression moder у - Вх е? where en No.62 we mean that no intercept point so Regression line passing the B. - Bate e -y-Bix f T.depedent vechodie Oxis venable Ba slople of the Regression line - ß :- homeling colled Regression coefficient The slope ß is the chang in the mean of distribution of y produced by a unique change in x. Here No intercept pornt Regression model obtain seems o apruprrate in analysis data from chemical & other manufacturing Посеѕѕ, - y = Bate: - given n observation (Ii, ti where 11,2

The least square function is ei= J; - Bxi somming and savoring both sides & eit- & TirBxi) - ③ differen harte wert ß ego no " - 2 E (Ji-Bax;)(x) = 0 2 to E (371-BX; ) Xi 22 & yixi - Bx; ² - 0 {Jixi - Bexil- Egix - BEX ² / B = {xigi {X² The estimeted of ß like above

for B The estimater & fitted of ß is Regression unbiased model is estimator of 6?- dr is - Elfi-5 ? nal moses - Slui - Ê / - Tizi 5 (9i-B) yox with a nal degree's of freedom