Jeff Phang
45 Tuesday
March 3, 2009
ARE 106 HW #6
1. Run a regression relating house prices to a constant, lajolla, bedrms, rooms, baths,
firepl, garage, pool, yard, and view (in this order, for ease in grading).
Report the results in standard format.
Model 1: OLS estimates using the 59 observations 159
Dependent variable: price
coefficient
std. error
tratio
pvalue

const
31.3355
45.5026
0.6887
0.4943
lajolla
132.235
19.1877
6.892
9.76E09 ***
bedrms
1.35268
15.2037
0.08897
0.9295
rooms
4.09467
11.5367
0.3549
0.7242
baths
36.6244
15.8076
2.317
0.0247
**
firepl
34.7332
17.7819
1.953
0.0565
*
garage
11.3213
15.8706
0.7133
0.4790
pool
30.6849
22.3680
1.372
0.1764
yard
0.00325721
0.00185451
1.756
0.0853
*
view
23.1777
18.9386
1.224
0.2269
Mean of dependent variable = 228.629
Standard deviation of dep. var. = 112.436
Sum of squared residuals = 214106
Standard error of the regression = 66.1022
Unadjusted Rsquared = 0.70799
Adjusted Rsquared = 0.65436
Fstatistic (9, 49) = 13.2006 (pvalue < 0.00001)
Loglikelihood = 325.52
Akaike information criterion (AIC) = 671.039
Schwarz Bayesian criterion (BIC) = 691.815
HannanQuinn criterion (HQC) = 679.149
Excluding the constant, pvalue was highest for variable 5 (bedrms)
Price
bar
=
31.3355 + 132.235(la jolla)+ 1.35268(bedrooms) +
(0.6887) (6.892)
(0.08897)
4.09467(rooms) + 36.6244(baths) + 34.7332(firepl) +
(
0.3549)
(2.317)
(1.953)
11.3213(garage) + 30.6849(pool) + 0.00325721(yard) +
(0.7133)
(30.6849)
(1.756)
23.1777(view)
(
1.224)
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2
= 0.71 σ
hat
= 66.10
Write the null and alternate hypotheses tested in the "goodness of fit" F test, and formally draw a conclusion.
Special wald test.
Ho: β2 = β 3 = β4 = β 5 = β 6 = β 7 = β 8 = β 9 = β 10 = 0
Ha: not Ho.
F stat = [(ESS
r
– ESS
u
)
/ q]/ [(ESS
u
)/ TK]
Analysis of Variance:
Sum of squares
df
Mean square
Regression
519120
9
57680
Residual
214106
49
4369.51
Total
733226
58
14963.8
R^2 = 519120 / 733226 = 0.707995
F(9, 49) = 57680 / 4369.51 = 13.2006 [pvalue 2.14e010]
F
c
(5910)
= 2.08
The probability of Ho being true when if we reject it is 2.14e010. Since F* = 13.2006 is greater than F
c
= 2.08 then we
reject the null.
Very briefly examine the model for plausibility.
It is difficult to isolate the effect that each of the variables has on price because there would be little to no houses without
a bedroom or a bathroom. It’s difficult to find a house that has no bedrooms, no bathrooms but a pool. It then becomes
very difficult to separate the effects of a bedroom or bathroom from a garage, pool or any other variable. This validity of
this model is questionable.
Are the signs of the variables as expected?
The signs of the variables are as expected. Holding all others constant, an increase in the # of bedrooms with the same
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 Winter '09
 Havenner
 Normal Distribution, Regression Analysis, Akaike information criterion

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