Question

sve v anu i, respectively. 7. Regression without any regressor. Suppose you are given the model: Y = pi + uj. Use OLS to find the estimator of Bi. What is its variance and the RSS? Does the estimated By make intuitive sense? Now consider the two-variable model Y = B1 + B2X; +ui. Is it worth adding X, to the model? If not, why bother with regression analysis?

Answer 1

Vues Y,= Betue - 0 Yo + B14 Bx, +4; —@ The sample regression as Yet 8 + ů, — : By using least square. poninciple. The minimined model a 12 S1 c By differentiating we get d (af) 2 {{4-8)=1). of Te 20. d d (üz) Value To same Sample Mean Å -ý - 6 variance of sample mean a mean -o ... Valiar

Te residual som of Square (4-4) - 24– cr at ons in a (n-1) heith addition of anothoe Variable fes Xp cawes to reduce then it is advisable to add more Variables. Unless, there is any relation blo Yg & Xq. The two variable model obtained from the - analysis of variance. RSS - Tss - Ess - E14 - Eůr 342 - FE 2 x;" where Res a residual sum of squales, Tss - Total Sum of squalo, Ess - Explamed Som of Squalen Be to be significant, Ros be lower in linear regression bodel with one Explanatory roodel. Variable than linear resion model with no Explanatory Variable. mod

An increase in Explanatory Variables en regression model there is decrease in Rss its coefficient may significant linear and