Age Gap Analysis
1. SPRICE: selling price of home, dollars
LIVAREA: living area, hundreds of square feet
AGE: number of beds
BEDS: number of baths
BATHS: =1 if lot size > .5 acres, 0 otherwise
LGELOT: age of home at time of sale, years
POOL: =1 if home has pool, 0 otherwise
| SPRICE | LIVAREA | AGE | BEDS | BATHS | LGELOT | POOL | Mean | 123693.9 | 16.75 | 21.86 | 3.29 | 2.13 | 0.06 | 0.07 | Median | 109500.0 | 16.00 | 19.00 | 3.00 | 2.00 | 0.00 | 0.00 | Maximum | 713000.0 | 49.00 | 97.00 | 6.00 | 6.50 | 1.00 | 1.00 | Minimum | 22000.00 | 7.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | Std. Dev. | 63250.89 | 5.46 | 13.11 | 0.62 | 0.53 | 0.24 | 0.25 |
2. A multiple regression model:
SPRICE=β1+β2LIVAREA+β3AGE+β4BEDS+β5BATHS+β6LGELOT+β7POOL …show more content…
β2: An increase of living area by a hundred of square feet increases the selling price of home by 8884.48 dollars. β3: A year increase in the age of the home decreases the selling price of home by 162.94 dollars. β4: A unit increase in the numbers of beds decreases the selling price of home by 10571.85 dollars. It is doubtful in the inverse change between price and numbers of beds for me because increasing beds will increase the area of the home, leading to increase the value of home. β5: A unit increase in the numbers of baths decrease the selling price of home by 3539.32 dollars. It is plausible for this situation since more baths would decrease the area of bedrooms or drawing room and so on when the total parallelogram is …show more content…
β7: A pool increases the value of a home by 14479.26 dollars.
SPRICE=160311.11+8884.48LIVAREA-162.94AGE-10571.85BEDS-3539.32BATHS (se) (6147.514) (281.1894) (75.75) (1870.12) (2720.869)
+ 59598.02LGELOT+ 14479.26POOL (4202.445) (3795.593)
3. Regression model:
SPRICE=β1+β2LIVAREA+δ1LIVAREA2+β3AGE+δ2AGE2+β4BEDS+ β5BATHS+β6LGELOT+β7POOL SPRICE=67308.27+3192.20LIVAREA+130.61LIVAREA2-640.72AGE+8.49AGE2 -8429.91BEDS-2619.38BATHS+51258.81LGELOT+14288.09POOL
The eviews output shows in Appendix. a. Marginal effect of AGE on SPRICE is
∂E(SPRICE)/ ∂AGE = β3+δ2AGE
The estimated response of price to age:
∂SPRICE/ ∂AGE = -640.72+8.48AGE
Substituting into this expression we find that when age is at its median value in the sample of 19 years, the marginal effect of age on sprice is
-640.72+8.48*19 = -485.11
The age of home on the 19 years old reduce $485.11 on the selling price of home.
b. The null hypothesis H0: β3=δ2=0
The alternative hypothesis H1: β3≠0, δ2≠0 or both are nonzero
If H0 is true: F = [(SSER-SSEU)/J]/[SSEU/(N-K)]
= [(SSER-SSEU)/2]/[SSEU/(1500-9)] ~ F ( 2,
LIVAREA: living area, hundreds of square feet
AGE: number of beds
BEDS: number of baths
BATHS: =1 if lot size > .5 acres, 0 otherwise
LGELOT: age of home at time of sale, years
POOL: =1 if home has pool, 0 otherwise
| SPRICE | LIVAREA | AGE | BEDS | BATHS | LGELOT | POOL | Mean | 123693.9 | 16.75 | 21.86 | 3.29 | 2.13 | 0.06 | 0.07 | Median | 109500.0 | 16.00 | 19.00 | 3.00 | 2.00 | 0.00 | 0.00 | Maximum | 713000.0 | 49.00 | 97.00 | 6.00 | 6.50 | 1.00 | 1.00 | Minimum | 22000.00 | 7.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | Std. Dev. | 63250.89 | 5.46 | 13.11 | 0.62 | 0.53 | 0.24 | 0.25 |
2. A multiple regression model:
SPRICE=β1+β2LIVAREA+β3AGE+β4BEDS+β5BATHS+β6LGELOT+β7POOL …show more content…
β2: An increase of living area by a hundred of square feet increases the selling price of home by 8884.48 dollars. β3: A year increase in the age of the home decreases the selling price of home by 162.94 dollars. β4: A unit increase in the numbers of beds decreases the selling price of home by 10571.85 dollars. It is doubtful in the inverse change between price and numbers of beds for me because increasing beds will increase the area of the home, leading to increase the value of home. β5: A unit increase in the numbers of baths decrease the selling price of home by 3539.32 dollars. It is plausible for this situation since more baths would decrease the area of bedrooms or drawing room and so on when the total parallelogram is …show more content…
β7: A pool increases the value of a home by 14479.26 dollars.
SPRICE=160311.11+8884.48LIVAREA-162.94AGE-10571.85BEDS-3539.32BATHS (se) (6147.514) (281.1894) (75.75) (1870.12) (2720.869)
+ 59598.02LGELOT+ 14479.26POOL (4202.445) (3795.593)
3. Regression model:
SPRICE=β1+β2LIVAREA+δ1LIVAREA2+β3AGE+δ2AGE2+β4BEDS+ β5BATHS+β6LGELOT+β7POOL SPRICE=67308.27+3192.20LIVAREA+130.61LIVAREA2-640.72AGE+8.49AGE2 -8429.91BEDS-2619.38BATHS+51258.81LGELOT+14288.09POOL
The eviews output shows in Appendix. a. Marginal effect of AGE on SPRICE is
∂E(SPRICE)/ ∂AGE = β3+δ2AGE
The estimated response of price to age:
∂SPRICE/ ∂AGE = -640.72+8.48AGE
Substituting into this expression we find that when age is at its median value in the sample of 19 years, the marginal effect of age on sprice is
-640.72+8.48*19 = -485.11
The age of home on the 19 years old reduce $485.11 on the selling price of home.
b. The null hypothesis H0: β3=δ2=0
The alternative hypothesis H1: β3≠0, δ2≠0 or both are nonzero
If H0 is true: F = [(SSER-SSEU)/J]/[SSEU/(N-K)]
= [(SSER-SSEU)/2]/[SSEU/(1500-9)] ~ F ( 2,