Finish the HW1.with quailty work

&DPO ����� $SPTT 4FDUJPO� .VMUJQMF 3FHSFTTJPO

1SPG� +BTPO #MFWJOT

%FQBSUNFOU PG &DPOPNJDT 5IF 0IJP 4UBUF 6OJWFSTJUZ

4JNQMF 3FHSFTTJPO /PUBUJPO

Ŕ 1SFWJPVTMZ XF IBWF CFFO VTJOH UIF TJOHMF�WBSJBCMF NPEFM

:J = β� + β�9J + VJ.

Ŕ 5IF J TVCTDSJQU SFQSFTFOUT B TJOHMF PCTFSWBUJPO� 'PS B EBUBTFU XJUI O PCTFSWBUJPOT XF IBWF O FRVBUJPOT�

:� = β� + β�9� + V�,

:� = β� + β�9� + V�, ���

:O = β� + β�9O + VO.

Ŕ 5IJT NPEFM POMZ BMMPXT GPS POF JOEFQFOEFOU WBSJBCMF 9J� Ŕ 5P BMMPX GPS NVMUJQMF JOEFQFOEFOU WBSJBCMFT JO PVS SFHSFTTJPO XF IBWF UP HFOFSBMJ[F UIF OPUBUJPO�

.VMUJQMF 3FHSFTTJPO /PUBUJPO

Ŕ &YUFOEJOH UP , SFHSFTTPST XF BEE B L TVCTDSJQU�

Ŕ 8F XSJUF UIF NPEFM GPS , SFHSFTTPST BOE O PCTFSWBUJPOT BT

:J = β� + β�9J� + β�9J� + · · · + β,9J,! "# $ , SFHSFTTPST

+VJ

Ŕ 8SJUJOH PVU UIF FOUJSF TZTUFN PG O FRVBUJPOT�

:� = β� + β�9�� + β�9�� + · · · + β�9�, + V�, :� = β� + β�9�� + β�9�� + · · · + β�9�, + V�, ���

:O = β� + β�9O� + β�9O� + · · · + β�9O, + VO.

*OUFSQSFUJOH .VMUJQMF 3FHSFTTJPO $PFťDJFOUT

Ŕ $PFťDJFOUT JO NVMUJQMF MJOFBS SFHSFTTJPO BSF DBMMFE UIF NVMUJQMF SFHSFTTJPO DPFťDJFOUT PS QBSUJBM SFHSFTTJPO DPFťDJFOUT�

Ŕ 1SFWJPVTMZ β� JO PVS TJOHMF�WBSJBCMF MJOFBS SFHSFTTJPO NPEFM SFQSFTFOUFE UIF DIBOHF JO UIF EFQFOEFOU WBSJBCMF BTTPDJBUFE XJUI B POF�VOJU JODSFBTF JO UIF EFQFOEFOU WBSJBCMF�

Ŕ )PMEJOH PUIFS WBSJBCMFT DPOTUBOU� /PX GPS TPNF WBSJBCMF 9L βL SFQSFTFOUT UIF JODSFBTF JO 9L BTTPDJBUFE XJUI B POF�VOJU JODSFBTF JO UIF L�UI EFQFOEFOU WBSJBCMF IPMEJOH UIF PUIFS JOEFQFOEFOU WBSJBCMFT DPOTUBOU�

&YBNQMF� 'JOBODJBM "JE

&YBNQMF 4UVEFONVOE ƈƆƇƆ Q� Ɗƈ

Ŕ '*/"*%J = BNPVOU PG ţOBODJBM BJE BXBSEFE EPMMBST QFS ZFBS

Ŕ 1"3&/5J = FYQFDUFE GBNJMZ DPOUSJCVUJPO EPMMBST QFS ZFBS

Ŕ )43"/,J = (1" SBOL JO IJHI TDIPPM QFSDFOUBHF Ɔ�ƇƆƆ XJUI ƇƆƆ CFJOH UIF IJHIFTU

'*/"*%J = β� + β�1"3&/5J + β�)43"/,J + VJ

&YBNQMF� 'JOBODJBM "JE DPOU�E

&YBNQMF

!'*/"*%J = ���� − �.�� 1"3&/5J + ��.� )43"/,J

Ŕ )FSF β̂� = −�.�� NFBOT UIBU IPMEJOH IJHI TDIPPM SBOL ţYFE TUVEFOUT XIPTF QBSFOUT DBO DPOUSJCVUF BO BEEJUJPOBM ƚƇ XJMM SFDFJWF PO BWFSBHF ƚƆ�Ɖƌ MFTT JO ţOBODJBM BJE�

Ŕ 'PS BO FYUSB ƚƇ ƆƆƆ JO FYQFDUFE QBSFOUBM DPOUSJCVUJPOT UIBUōT ƚƉƌƆ MFTT JO ţOBODJBM BJE�

Ŕ �ƚƉƌƆ � ƚƇ ƆƆƆ × �Ɔ�Ɖƌ�

Ŕ #FDBVTF PG MJOFBSJUZ UIJT JT UIF FTUJNBUFE FŢFDU GPS CPUI IJHI BOE MPX SBOLFE TUVEFOUT�

(FPNFUSZ PG .VMUJQMF 3FHSFTTJPO

-0.36

HSRANK

HSRANK

FI N A ID

FI N A ID

FI N A ID

PARENT

PA RE NT

87.4

'JHVSF Ƈ� (FPNFUSJD JOUFSQSFUBUJPO PG NVMUJQMF SFHSFTTJPO

5IF $PFťDJFOU PG %FUFSNJOBUJPO

Ŕ 5IF NPTU DPNNPO NFBTVSF PG UIF PWFSBMM ţU PG B SFHSFTTJPO JT UIF DPFťDJFOU PG EFUFSNJOBUJPO EFOPUFE 3��

Ŕ 5IJT NFBTVSF TVNNBSJ[FT UIF ţU PG B TJOHMF SFHSFTTJPO JOEFQFOEFOUMZ�

Ŕ *U JT BMTP VTFGVM UP DPNQBSF UIF ţU PG B DPMMFDUJPO PG SFHSFTTJPOT XJUI EJŢFSFOU DPNCJOBUJPOT PG JODMVEFE JOEFQFOEFOU WBSJBCMFT�

%FDPNQPTJUJPO PG 7BSJBODF

Ŕ 5P EFţOF 3� XF VTF UIF EFDPNQPTJUJPO PG WBSJBODF� Ŕ 445 JT UIF UPUBM WBSJBUJPO JO :J UIF UPUBM TVN PG TRVBSFT�

445 ≡ O%

J=�

(:J − :̄)�.

Ŕ 445 DBO CF GBDUPSFE JOUP UXP DPNQPOFOUT BT 445 = 44& + 443� Ƈ� 44& DBQUVSFT EFWJBUJPOT JO :J GSPN UIF NFBO :̄

44& ≡ O%

J=�

(:̂J − :̄)�

ƈ� 443 DBQUVSJOH UIF ŏVOFYQMBJOFEŐ PS SFTJEVBM EFWJBUJPOT

443 ≡ O%

J=�

(:J − :̂J)�

%FDPNQPTJUJPO PG 7BSJBODF

.BUIFNBUJDBMMZ�

445 = O%

J=�

(:J − :̄)�

= O%

J=�

(:J − :̂J)� + O%

J=�

(:̂J − :̄)�

= O%

J=�

V̂�J + O%

J=�

(:̂J − :̄)�

= 443 + 44&.

*O PUIFS XPSET NPSF JO MJOF XJUI PVS SFHSFTTJPO GPSN �

445 = 44& + 443.

6OBEKVTUFE 3�

Ŕ 5IF DPFťDJFOU PG EFUFSNJOBUJPO JT EFţOFE BT

3� = 44& 445

= � − 443 445

.

Ŕ *U JT UIF GSBDUJPO PG UPUBM WBSJBUJPO JO :J J�F� 445 UIBU JT FYQMBJOFE CZ UIF JODMVEFE SFHSFTTPST J�F 44& �

Ŕ .FBTVSFT TVDI BT 3� BSF DBMMFE HPPEOFTT PG ţU NFBTVSFT�

Ŕ " IJHIFS WBMVF PG 3� JOEJDBUFT UIBU UIF SFHSFTTJPO ţUT UIF EBUB CFUUFS TJODF 9 DBO FYQMBJO NPSF PG UIF WBSJBUJPO JO :�

" 1SPCMFN XJUI 3�

Ŕ 8IFO BEEJOH B WBSJBCMF 3� BMXBZT JODSFBTFT�

Ŕ 5IJT IBQQFOT DBO IBQQFO FWFO JG UIF WBSJBCMF JT VOSFMBUFE�

Ŕ 5P TFF UIJT SFDBMM UIBU

3� = 44& 445

.

Ŕ 445 JT B GVODUJPO PG :J POMZ TP JU JT VODIBOHFE�

Ŕ #VU BEEJOH BO BEEJUJPOBM 9 WBSJBCMF UP UIF SFHSFTTJPO XFBLMZ JODSFBTF 44& BOE IFODF 3��

Ŕ 5IFSFGPSF MPPLJOH BU 3� BMPOF DBO FODPVSBHF UIF BEEJUJPO PG UPP NBOZ FYQMBOBUPSZ WBSJBCMFT�

"EKVTUFE 3�

Ŕ 5IF BEKVTUFE 3� JT EFţOFE BT

3̄� = � − 443/(O − , − �) 445/(O − �)

.

Ŕ 5IFSF JT B ŏQFOBMUZŐ JO UIF TFOTF UIBU JODSFBTJOH UIF OVNCFS PG SFHSFTTPST , EFDSFBTFT 3̄� VOMFTT UIF 443 EFDSFBTFT 44& JODSFBTFT FOPVHI UP DPNQFOTBUF�

Ŕ *OUVJUJWFMZ UIF BEKVTUFE 3� NFBTVSFT UIF QFSDFOUBHF PG UIF WBSJBUJPO JO : BSPVOE :̄ UIBU JT FYQMBJOFE CZ UIF SFHSFTTPST XJUI BO BEKVTUNFOU GPS UIF EFHSFFT PG GSFFEPN�

3̄� .BZ *ODSFBTF PS %FDSFBTF

Ŕ "T PQQPTFE UP UIF TUBOEBSE 3� 3̄� NBZ JODSFBTF EFDSFBTF PS TUBZ UIF TBNF XIFO BO BEEJUJPOBM SFHSFTTPS JT BEEFE�

Ŕ 5IF EJSFDUJPO PG UIF DIBOHF XJMM EFQFOE PO XIFUIFS UIF ţU JNQSPWFT FOPVHI UP KVTUJGZ UIF EFDSFBTF JO UIF EFHSFFT PG GSFFEPN�

Ŕ "T XJUI 3� 3̄� JT CPVOEFE BCPWF CZ Ƈ�Ɔ�

Ŕ )PXFWFS JU NBZ BMTP CF OFHBUJWF XIJMF UIF NJOJNVN QPTTJCMF 3� JT Ɔ�

0SEJOBSZ -FBTU 4RVBSFT 3FHSFTTJPO JO 4UBUB

Ŕ 0SEJOBSZ MFBTU TRVBSFT� 5P SVO 0-4 JO 4UBUB VTF UIF ß�¨ß�ãã DPNNBOE GPMMPXFE CZ UIF EFQFOEFOU WBSJBCMF BOE UIFO UIF JOEFQFOEFOU WBSJBCMFT� 'PS FYBNQMF� ß�¨ß�ãã ā Ā΁ Ā΂�

Ŕ 'JUUFE WBMVFT� 5P HFOFSBUF B OFX WBSJBCMF TBZ ā­�ê DPOUBJOJOH UIF ţUUFE WBMVFT SVO Üß��°�ê ā­�êϔ Ā� GPMMPXJOH UIF ß�¨ß�ãã DPNNBOE�

Ŕ 3FTJEVBMT� 5P HFOFSBUF B OFX WBSJBCMF TBZ ï­�ê DPOUBJOJOH UIF SFTJEVBMT SVO Üß��°�ê ï­�êϔ ß�ã°� GPMMPXJOH UIF ß�¨ß�ãã DPNNBOE�

4UBUB &YBNQMF� *OQVU

ïã� §°É�°� ß�¨ß�ãã §°É�°� Ü�ß�Éê ­ãß�É¿ Üß��°�ê ā­�êϔ Ā� Üß��°�ê ï­�êϔ ß�ã°�

4UBUB &YBNQMF� 0VUQVU

. use finaid

. regress finaid parent hsrank

Source SS df MS Number of obs = 50 F(2, 47) = 68.33

Model 1.0496e+09 2 524779682 Prob > F = 0.0000 Residual 360941186 47 7679599.7 R-squared = 0.7441

Adj R-squared = 0.7332 Total 1.4105e+09 49 28785725.5 Root MSE = 2771.2

finaid Coef. Std. Err. t P>|t| [95% Conf. Interval]

parent -.3567721 .0316851 -11.26 0.000 -.4205143 -.2930299 hsrank 87.37815 20.67413 4.23 0.000 45.78717 128.9691 _cons 8926.929 1739.083 5.13 0.000 5428.346 12425.51

. predict yhat, xb

. predict uhat, resid