. 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

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:

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.