. Estimating a Regression

The regression is also based on the University town real estate data. The regression is:

price = ві + 61utown + P2sqft + 7(sqft x utown)

+вз age + 62pool + 63fpla. ce + e

The estimated model is

Подпись: Mean dependent var 247.6557 Sum squared resid 230184.4 R2 0.870570 F(6, 993) 1113.183 Log-likelihood -4138.379 Schwarz criterion 8325.112
image209

OLS, using observations 1-1000
Dependent variable: price

Coefficient

Std. Error

t-ratio

p-value

const

24.5000

6.19172

3.9569

0.0001

utown

27.4530

8.42258

3.2594

0.0012

sqft

7.61218

0.245176

31.0477

0.0000

sqft_utown

1.29940

0.332048

3.9133

0.0001

age

-0.190086

0.0512046

-3.7123

0.0002

pool

4.37716

1.19669

3.6577

0.0003

fplace

1.64918

0.971957

1.6968

0.0901

The coefficient on the slope indicator variable sqft x utown is significantly different from zero at the 5% level. This means that size of a home near the university has a different impact on average home price. Based on the estimated model, the following conclusions are drawn:

• The location premium for lots near the university is $27,453

• The change in expected price per additional square foot is $89.12 near the university and $76.12 elsewhere

• Homes depreciate $190.10/year

• A pool is worth $4,377.30

• A fireplace is worth $1649.20

The script that generates these is:

1 scalar premium = $coeff(utown)*1000

2 scalar sq_u = 10*($coeff(sqft)+$coeff(sqft_utown))

3 scalar sq_other = 10*$coeff(sqft)

4 scalar depr = 1000*$coeff(age)

5 scalar sp = 1000*$coeff(pool)

6 scalar firep = 1000*$coeff(fplace)

7 printf "n University Premium = $%8.7gn

8 Marginal effect of sqft near University = $%7.6gn

9 Marginal effect of sqft elsewhere = $%7.6gn

10 Depreciation Rate = $%7.2fn

11 Pool = $%7.2fn

12 Fireplace = $%7.2fn",premium, sq_u, sq_other, depr, sp, firep

Notice that most of the coefficients was multiplied by 1000 since home prices are measured in $1000 increments. Square feet are measured in increments of 100, therefore its marginal effect is multiplied by 1000/100 = 10. It is very important to know the units in which the variables are recorded. This is the only way you can make ecnomic sense from your results.

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