Sales Value of Residential Property

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1 Sales Value of Resdental Property y = b X D2 +b D3 +b A y = sales value of the property (dollars) X = square feet of lvng space D1=dummy vble for one bedroom home D2=dummy vble for two bedroom home D3=dummy vble for three bedroom home A1=dummy vble for one bathroom home A2=dummy vble for two bathroom home For a one-bedroom, one-bathroom home, such that D2=0, D3=0, and A2=0, we have: y = b 1 2 X 1 bedroom, 1 bathroom

2 sellng prce y b 1 +b 4 +b 5 b 1 +b 4 b 1 +b 3 +b 5 House Sales Model wth Restrcted Intercepts y = b 1 2 X 3 D2 4 D3 5 A2 D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 1 +b 3 b 1 +b 5 b 2 b 1 0 X square feet of lvng space

3 Sales Value of Resdental Property y = b 1 2 X 3 D2 +b 4 D3 +b 5 A2 For a 2-bedroom, 1-bathroom home, we have D2=1, D3=0, and A2=0 y = (b 1 3 ) 2 X 2 bedroom, 1 bathroom

4 Sales Value of Resdental Property y = b 1 2 X 3 D2 4 D3 5 A2 For a 1-bedroom, 2-bathroom home, we have D2=0, D3=0, and A2=1 y = (b 1 5 ) 2 X 1 bedroom, 2 bathroom

5 Sales Value of Resdental Property y = b 1 2 X 3 D2 4 D3 5 A2 For a 2-bedroom, 2-bathroom home, we have D2=1, D3=0, and A2=1 y = (b ) 2 X 2 bedroom, 2 bathroom y = (b ) 2 X 3 bedroom, 2 bathroom y = (b 1 4 ) 2 X 3 bedroom, 1 bathroom

6 Sales Value of Resdental Property y = b 1 2 X 3 D2 4 D3 5 A2 y = sales value of the property (dollars) X = square feet of lvng space D1=dummy vble for one bedroom home D2=dummy vble for two bedroom home D3=dummy vble for three bedroom home A1=dummy vble for one bathroom home A2=dummy vble for two bathroom home D2A2 = nteracton two-bed & two-bath D3A2 = nteracton three-bed & two-bath y = β 1 + β 2 X + β 3 D2 + β 4 D3 + β 5 A2 + β 6 D2A2 + β 7 D3A2

7 Ths one equaton wth all these dummy varables actually s representng sx equatons. You must substtute n for each of the dummy varables n order to generate the sx equatons that are mpled by ths one dummy varable equaton. y = b 1 2 X 3 D2 4 D3 5 A2 6 D2A2 7 D3A2 For a one-bedroom, one-bathroom home, such that D2=0, D3=0, and A2=0, we have: y = b 1 2 X 1 bedroom, 1 bathroom

8 House Sales Model wth Unrestrcted Intercepts sellng prce y D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 2 b 1 0 X square feet of lvng space

9 y = β 1 + β 2 X + β 3 D2 + β 4 D3 + β 5 A2 + β 6 D2A2 + β 7 D3A2 two-bedroom, one-bathroom D1=0, D2=1, D3=0 and A1=1, A2=0 y = (β 1 + β 3 ) + β 2 X 2 bedroom, 1 bathroom now graph t! =======>

10 House Sales Model wth Unrestrcted Intercepts sellng prce y D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 1 +b 3 b 1 0 X square feet of lvng space

11 y = b 1 2 X 3 D2 4 D3 5 A2 6 D2A2 7 D3A2 one-bedroom, two-bathroom D1=1, D2=0, D3=0 and A1=0, A2=1 y = (b 1 5 ) 2 X 1 bedroom, 2 bathroom now graph t! =======>

12 House Sales Model wth Unrestrcted Intercepts sellng prce y D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 1 +b 3 b 1 +b 5 b 1 0 X square feet of lvng space

13 y = b 1 2 X 3 D2 4 D3 5 A2 6 D2A2 7 D3A2 two-bedroom, two-bathroom D1=0, D2=1, D3=0 and A1=0, A2=1 y = (b b 6 ) +b 2 X 2 bedroom, 2 bathroom now graph t! =======>

14 House Sales Model wth Unrestrcted Intercepts sellng prce y b 1 +b 3 +b 5 +b 6 D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 1 +b 3 b 1 +b 5 b 1 0 X square feet of lvng space

15 House Sales Model wth Unrestrcted Intercepts sellng prce y b 1 +b 4 +b 5 +b 7 b 1 +b 4 b 1 +b 3 +b 5 +b 6 D3-A2 (three bed, two bath) D3-A1 (three bed, one bath) D2-A2 (two bed, two bath) D2-A1 (two bed, one bath) D1-A2 (one bed, two bath) D1-A1 (one bed,one bath) b 1 +b 3 b 1 +b 5 b 1 0 X square feet of lvng space

16 How do we create composte dummy varables? Bathrooms Want to account for nteracton between race and gender. 1 2 Bedrooms

17 Garage vs. Bedrooms vs. Bathrooms Bedrooms Baths: Garage

18 Karnaugh Map for Garage, Bedrooms, Bathrooms, and School Dstrct: Bedrooms S C H O O L A B Baths: Garage all Garage all

19 Composte dummy varables are created for each nonempty cell. Create four composte dummy varables: D1A1=1 f one bedroom, one bath; D1A2=1 f one bedroom, two bath; D2A1=1 f two bedroom, one bath; D2A2=1 f two bedroom, two bath;.

20 Testng effect of 2nd Bathroom on Sales Value: Y ˆ = b X S S X H 0 : β 3 0 vs. H 1 : β 3 > 0 H 0 : β 5 0 vs. H 1 : β 5 > 0 b 3 Est. Varb 3 t n 4 b 5 Est. Var b 5 tn 4

21 Testng Ho: β3 = β5 = 0 H1 : otherwse (SSE R SSE U )/ 2 SSE U /(n 4) F 2 n 4 and n =1 SSE U = (y b 1 b 2 X b 3 S b 5 S X ) 2 n SSE R = (y b 1 b 2 X ) 2 = 1

22 Sale of House wth Bed and Bath Dummes PRICE = f ( SQFEET, D2BED, B3BED, A2BATH ) I. SQFEET = square feet of lvng space II. D2BED = dummy=1 f two-bedroom house III. D3BED = dummy=1 f three-bedroom house IV. A2BATH = dummy=1 f two-bathroom house I. II. III. IV. PRICE (thousands)

23 Sale of House wth Bed and Bath Dummes PRICE = f ( SQFEET, D2BED, B3BED, A2BATH ) DEP VAR: PRICE N: 10 MULTIPLE R: SQUARED MULTIPLE R: ADJUSTED SQUARED MULTIPLE R: STD ERROR OF ESTIMATE: 3.40 VARIABLE COEFF STD ERR T P(2-TAIL) INTERCEPT SQFEET D2BED D3BED A2BATH ( for 1,000 square feet: = or $14,518 )

24 Regresson Analyss of Sale of Resdental Property VARIABLE COEFF STD ERR T P(2-TAIL) INTERCEPT SQFEET D2BED D3BED A2BATH for 1,000 square feet: = or $14,518 add a bathroom: $14,518 4,883 $19,401 add a bedroom: $14,518 14,662 $29,180 add 2 bedrooms: $14,518 29,803 $44,321 add bath and 2 bedrooms: 14, , ,803 = $49,204

25 Sale of House wth Bed and Bath Dummes PRICE = f ( SQFEET, D2BED, B3BED, A2BATH ) DEP VAR: PRICE N: 10 MULTIPLE R: SQUARED MULTIPLE R: ADJUSTED SQUARED MULTIPLE R: STD ERROR OF ESTIMATE: 3.40 ANALYSIS OF VARIANCE SOURCE SUM-OF-SQUARES DF MEAN-SQ F-RATIO P REGRESSION RESIDUAL DURBIN-WATSON D STATISTIC: FIRST ORDER AUTOCORRELATION COEFF:

26 Plot of House Prce x Square Feet 150 bgger houses cost more! 100 PRICE SQFEET

27 Plot of Orgnal Data Ponts SYSTAT GRAPH PRICE SQFEET

28 Plot Prce of 1 & 2 Bathroom Houses SYSTAT GRAPH thousand $ looks lke a fxed upward shft n prce! PRICE A2BATH

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