= , R indicates what is the fraction of the total

Transcription

1 Aswe key to homewok o. Questo ) a) ( )( Y Y ) ( ) x y x Y SSR b) R. 8 R dcates what s the facto of the total SST 33.7 vaato that ca be explaed by the model. c) Va[ ] Questo u ( ) 65.5 MLR. (Lea Paametes) Y... k k s satsfed MLR. (Radom Samplg) Radom sample of obsevatos (... Y ) k We assume adom samplg. MLR.3 (o Pefect Colleaty) I the sample o of the depedet vaables s costat ad thee ae o exact lea elatoshps amog the depedet vaables. Ths s satsfed because of the way s daw gve. MLR.4 (Zeo Codtoal Mea) ( x x... ) x k Theoem 3. (Ubasedess of the OLS). Ths s satsfed fom the assumpto.

2 The estmato s ( )( y y) ( ) ( ) umeato y ( )[ ( x ) x u ]... k k ( ) ( ) ( ) ( ) Because s the esduals ad x γx... γ k γ x s the ftted value they ae ucoelated to each othe ad ( ) ( x ) Fo the same easo ( ) x ( ) x ( ) x ( ) x k k k k k Togethe the umeato: ( ) y ( )( ) ( ) So ( )( y y) ( ) ( ) ( ) ( ) ( ) u

3 ( ) ( ) ow let s take the expectato. Because [ ] [ ] [ ] ( ) ( ) b) s based. Suppose to be the OLS estmates. The because both esduals have zeo aveage Y. Also sce s also the esdual of the egesso. Theefoe. Fom the ubasedess of the OLS estmates [ ] [ ] s ubased f Questo 3 ) Vaable Obs. Mea Std. Dev. M Max House pce Gaage dummy o. of ooms Ut Sq. Feet Owe sgle Owe age Owe come o. depedets Mdwest South West

4 ) Vaables Coef. Std. o t P-value Costat Gaage dummy o. of ooms Ut Sq. feet R.83 Sample sze: 365 The aual pce of a gaage whch s estmated to be $79 s lkely to be based upwads because gaage cludes houses whch have multple gaages. Aual pce pe oom seems to be low compaed to the stadad aual et of a oom a apatmet. Ths could be because houses ae usually located lowe popety value aeas such as sububs. egatve costat tem could be due to the fact that depedet vaables such as o. of ooms o ut squae feet ae dstbuted fa away fom zeo. Hece thee s o data aoud whch ps dow the tecept. Because a compettve maket pces ae gve ad the same fo each dvdual egadless of hs/he pesoal chaactestcs they do ot ete the egesso o the RHS. 3) Mdwest Coef. Std. o t P-value Costat Gaage dummy o. of ooms Ut Sq. feet R.4 sample sze: 699 South Coef. Std. o t P-value Costat Gaage dummy o. of ooms Ut Sq. feet R.434 sample sze: 6 West Coef. Std. o t P-value Costat Gaage dummy o. of ooms Ut Sq. feet

5 R.83 sample sze: 63 otheast Coef. Std. o t P-value Costat Gaage dummy o. of ooms Ut Sq. feet R.379 sample sze: 593 What we ca see s that the pces of chaactestcs vay sgfcatly acoss dffeet egos of the U.S. Pces of gaages ae most expesve the West ad otheast. Ths could be ethe due to the fact that thee houses have moe gaages that s the umbe of automobles pe household could be hgh. It s emakable that gaages ae vey cheap the South. That could be due to the fact that the cost of buldg t s low sce they may ot eed heatg etc. I the Mdwest both pces of ooms ad ut squae feet ae low dcatg low housg costucto cost. I the West pce pe oom s emakably low ad at the same tme pce pe ut squae s the hghest. Ths would mea that ooms the West have smalle sze. Hgh costat tem the West also dcates the elatvely hgh popety value thee. Vaables Coef. Std. o t P-value Costat Gaage dummy o. of ooms o. of ooms sq Ut Sq. feet Ut sq. feet sq. 3.37e R.83 sample sze: 365 The fact that o. of ooms squaed ad ut squae feet squaed etes postvely meas that the magal pce of ooms ad squae feet ceases wth the umbe of ooms ad squae feet. That s houses wth moe ooms ae lkely to have hghe qualty ooms ad smlaly houses wth moe ut squae feet have hghe qualty doo space. But those effects ae both sgfcat at 5% sgfcace level. Ths s lkely to be patly due to the multcolleates betwee the umbe of ooms ad the umbe of ooms squae ad betwee the ut squae feet ad the ut squae feet squaed.