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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 Ïƒ2.

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 Î²2, Î²4 and Î´6. 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

âˆ’0.0226220

0.0171271

âˆ’1.321

age

âˆ’0.00802360

0.000511656

âˆ’15.68

owner

0.0958014

0.0179780

5.329

trad

âˆ’0.0731258

0.0175943

âˆ’4.156

sq_1000

âˆ’0.292309

0.0642581

âˆ’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

âˆ’0.0329058

0.0172464

âˆ’1.908

0.0567

age

âˆ’0.00803362

0.000523754

âˆ’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

âˆ’0.0208702

0.0254469

âˆ’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

âˆ’0.0337353

0.0102660

âˆ’3.286

0.0010

trad

âˆ’0.0389965

0.0100469

âˆ’3.881

0.0001

sq_1000

âˆ’0.00199492

0.0366933

âˆ’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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