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(Solved) Part B The following model shows the relationship between house prices and a number of explanatory variables. The model is estimated by OLS. Model 1


Question 6 only. Using an model to predict value given certain variables. Working needed. Thanks

Part B
The following model shows the relationship between house prices and a number of explanatory
variables. The model is estimated by OLS.
Model 1
,_1:"/3% = '( + '* $8=;% + '0 >4:?$% + '2 6#3% + @5 AB.3: + @7 ;:64 + @9 $8_1000 + <%
price
= house price, dollars.
sqft
= total living area in square feet
bdrms
= number of bedrooms
age
= age in years
owner
= 1 if owner occupied at sale; = 0 if vacant or tenant
trad
= 1 if traditional style; = 0 if other, such as townhouse, contemporary, etc.
sq_1000
= 1 if sqft < 1000; = 0 otherwise.
l_price
= log house price
Assume that the random error terms follow a normal distribution with mean zero and variance σ2.
Use the Gretl output on pages 9 and 10 to answer the questions in this part.
(To answer the questions regarding hypothesis test, you must provide the null and alternative
hypotheses, test statistic, the distribution of the test statistic under the null and the degrees of freedom,
critical value(s), decision rule and your conclusion.) 1. Interpret the estimated slope coefficients β2, β4 and δ6. 2. Is there evidence to indicate that traditional-style homes are less expensive than the
other type homes? Use the 1% significance level. Follow all the steps explained above,
and clearly state your conclusion. 3. Compute the elasticity of price with respect to sqft at the mean values and interpret
your answer. 4. Test whether all three dummy variables, owner, trad and sq_1000 are jointly
significant at the 5% significance level. Follow all the steps explained above and
clearly state your conclusion. 5. Test the overall significance of the model at the 5% significance level and clearly state
your conclusion. Follow all the steps explained above and clearly state your
conclusion. 6. Using the equation, predict the value of a traditional style house with 2500 square feet
of area, that is 20 years old, owner-occupied at the time of sale and that has 3
bedrooms. 7. Examine the model for evidence of a violation of any assumptions of the multiple
regression model. Clearly state the implications, if any, of the assumption being
violated in the model. 8 Gretl Output
Summary statistics price
sqft
bdrms
age
l_price n
1080
1080
1080
1080
1080 Mean
154860
2325.9
3.1796
19.574
11.795 Median
130000
2186.5
3.0000
18.000
11.775 Minimum
22000.
662.00
1.0000
1.0000
9.9988 Maximum
std.Dev.
1580000
122910
7897.0
1008.1
8.0000
0.7095
80.000
17.194
14.273
0.5245 Correlation Coefficients
Correlation Coefficients, using the observations 1 - 1080
5% critical value (two-tailed) = 0.0597 for n = 1080
price
1.0000 sqft
0.7607
1.0000 bdrms
0.4552
0.6846
1.0000 age
-0.2086
-0.1380
-0.1681
1.0000 l_price
0.8184
0.7904
0.5368
-0.3642
1.0000 price
sqft
bdrms
age
l_price Regression output
Model : OLS, using observations 1-1080
Dependent variable: l_price
coefficient
std. error
t-ratio
-----------------------------------------------const
11.1328
0.0445632
249.8
sqft
0.000382487
1.21821e-05
31.40
bdrms
−0.0226220
0.0171271
−1.321
age
−0.00802360
0.000511656
−15.68
owner
0.0958014
0.0179780
5.329
trad
−0.0731258
0.0175943
−4.156
sq_1000
−0.292309
0.0642581
−4.549
Mean dependent var
Sum squared resid
R-squared
F(6, 1073) 11.79518
85.92118
0.710579
439.0664 S.D. dependent var
S.E. of regression
Adjusted R-squared
P-value(F) 0.524535
0.282976
0.708960
9.5e-285 9 Restricted model: Regression output
OLS, using observations 1-1080
Dependent variable: l_price
coefficient
std. error
t-ratio
p-value
----------------------------------------------------------const
11.1076
0.0450090
246.8
0.0000
sqft
0.000408210
1.20810e-05
33.79
3.51e-171
bdrms
−0.0329058
0.0172464
−1.908
0.0567
age
−0.00803362
0.000523754
−15.34
3.58e-48
Mean dependent var
Sum squared resid
R-squared
F(3, 1076) 11.79518
91.40426
0.692109
806.2486 S.D. dependent var
S.E. of regression
Adjusted R-squared
P-value(F) 0.524535
0.291459
0.691251
1.2e-274 Auxiliary regression:
EGF = HI + HG JKLMF + HN OPQRJF + HS TUVF + HW XYZVQF + H[ MQTP + H JK_I]]] + ^F OLS, using observations 1-1080
Dependent variable: sq_u
coefficient
std. error
t-ratio
p-value
----------------------------------------------------------const
−0.0208702
0.0254469
−0.8201
0.4123
sqft
1.15223e-05
6.95636e-06
1.656
0.0979
bdrms
0.0105720
0.00978009
1.081
0.2800
age
0.00396228
0.000292171
13.56
8.72e-39
owner
−0.0337353
0.0102660
−3.286
0.0010
trad
−0.0389965
0.0100469
−3.881
0.0001
sq_1000
−0.00199492
0.0366933
−0.05437
0.9567
Mean dependent var
Sum squared resid
R-squared
F(6, 1073) 0.079557
28.01678
0.159988
34.06036 S.D. dependent var
S.E. of regression
Adjusted R-squared
P-value(F) 0.175815
0.161588
0.155290
9.05e-38 10

 


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