Question

Suppose that n = 193 i.i.d. observations for (Y, Xiyield the following regression results: ŷ = 33.48 +66.71X, SER = 15.96, R² = 0.72 (15.5) (12.7) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 386 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following estimated parameters change as result? (Check all that apply) A. The R of the regression. B. The estimated intercept and slope. LYC. The standard error of the regression (SER). LYD. The standard errors of the estimated coefficients. Using the 386 observations, what results will be produced by his regression program? û = 33.48 + 66.71X, SER=, R = 0.72 O, O (Round your responses to two decimal places)

Answer 1

Ang Ans - 33 4 4 6 + 7] * SER = 15.96 R = 0.72 na 193 Now Anothes a Beaches is int 6e4ed in the same regression free be make an Gewer when be enters the data into the regression. He Enter Each obsGuation twice so he has 386 obsGuations 01 Which of the following estimated parametes Change aga ose suet ? Ang : option c: Option D : The Standard Gros of the Regression CSER) The Standard Gowns of the estimated coefficients: no 386 Regsession line ✓ = 33.48 +66.71% R?: 017? sxx As B = Sxy sxy = Exixi-nexi sy, Sxx = Exi? - nisxi)? 1. we see that Biold - Bi new they sxycie, a sxy cold) I sxx nned with CamScanner = asxx

Similarly 2 new = R caldo - 0.72 R²= Sxy sxx Syy 21 R = 5+4 we get syy= 25xy Sxy 2 SxÝ Syys S SER= -15196 SER: Syy- Sky -15:46 - 0 ste= sy's - (sky)? - . Sxx X a SX X into new to old I converting it 2 = asyy - 2 SEP Sxy asxY Sxx = 2 ( Syy- Sty ) - 2 SER cold ) from I weget = ax 15.96 = 131192) My SER= 31.92 now Standard = Power of the estimated Coefficients Scanned with CamScanner

SE(Bo) = 12 12 Ó" SER Nem m= 2 Cruumber of variable) N = Total number of observationg ] SECÊ ) = SER N-a XSXX we find a relation between SECBI) (new) and Sec B ald ح SECBU: SER! SER' ✓ (386-2) 5xx XSER SER 38Чx x x V 384 sxx ah SECR) aed = 12,7 12,7 sed = .SE Serie V (193-2) Sxy SER 1Sxx Thes SECB) = SE R* 14 ། 384 X191 XSXX SER 191 J 79 1 Sxx J 384 = SECB) x 0.7052630 P.) 3 1217 XO'7052630 18195684 CSscanned with Camscanner

SEC = 1 SEP' xret a V 384 386 Ss SECBO)=1515 SER SX X Josep Cias ] = 15:5 - 37596"(that came= 15.5 ant (19.09.22This 28751671 193 Sxx 0109 3560 28 Sxx Now 29569 311g + a229 ) SEC 386 d 384 sắc ) ( 333 ( SÉCRO) = | 1019315757 New R=0,72 ī Ang . = 33.48466.71% SEP = 31.92 C 110-93] ) ( 18:96) Jo 93 CScanned with CamScanner