Econometrics. a Regression Analysis

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Question 1:
Run the regression Report your answer in the format of equation 5.8 (Chapter 5, p. 152) in the textbook including and the standard error of the regression (SER). Interpret the estimated slope parameter for LOT. In the interpretation, please note that PRICE is measured in thousands of dollars and LOT is measured in acres.

Model 1: OLS estimates using the 832 observations 1-832
Dependent variable: price

VARIABLE COEFFICIENT STDERROR T STAT P-VALUE

const 119.575 1.54566 77.362 <0.00001 *** lot 1.38850 0.209083 6.641 <0.00001 ***

Mean of dependent variable = 122.076
Standard deviation of dep. var. = 44.3478
Sum of squared residuals = 1.55189e+006
Standard error of residuals = 43.2406
Unadjusted R-squared = 0.05045
Adjusted R-squared = 0.04931
Degrees of freedom = 830
Log-likelihood = -4313.52
Akaike information criterion (AIC) = 8631.03
Schwarz Bayesian criterion (BIC) = 8640.48
Hannan-Quinn criterion (HQC) = 8634.66

PRICEi=119.575+1.3885LOTi,
1.54566 (0.209083)
R2=0.05045, SER=43.2406

Slope coefficient = 1.3885

* After analyzing the slope coefficient, one can assume that a one unit (one acre) change in lot would lead to an overall predicted change in price of $1388.50.

Question 2:
Now run the regression
Report your answer using the format of equation 5.8 (Chapter 5) in the textbook, including and SER. Interpret the estimated slope parameter for LOT. Also report the ANOVA table provided by GRETL (for use in answering question (9) below). In the interpretation, please note that PRICE is measured in thousands of dollars and LOT is measured in acres

Model 2: OLS estimates using the 832 observations 1-832
Dependent variable: price

VARIABLE COEFFICIENT STDERROR T STAT P-VALUE

const 34.6160 4.74177 7.300 <0.00001 *** lot 1.71129 0.148643 11.513 <0.00001 *** bdrm 3.39579 1.36729 2.484 0.01320 ** bthrm 20.9553 2.03989 10.273 <0.00001 *** gar 17.1107 1.32157 12.947 <0.00001 *** fplace 10.4375 1.59493 6.544 <0.00001 *** bsmt 12.2228 3.03260 4.030 0.00006 ***

Mean of dependent variable = 122.076
Standard deviation of dep. var. = 44.3478
Sum of squared residuals = 766332
Standard error of residuals = 30.4777
Unadjusted R-squared = 0.53111
Adjusted R-squared = 0.52770
F-statistic (6, 825) = 155.745 (p-value < 0.00001)
Log-likelihood = -4019.98
Akaike information criterion (AIC) = 8053.96
Schwarz Bayesian criterion (BIC) = 8087.03
Hannan-Quinn criterion (HQC) = 8066.64

PRICEi=34.616+1.71129LOTi+3.39579BDRMi+20.9553BTHRMi+17.1107GARi+10.4375FPLACEi+12.2228BSMTi

R2=0.531115, SER=30.4777

Slope coefficient = 1.77129

* After analyzing the slope coefficient, it can be assumed that a one unit (one acre) change in lot would lead to a predicted change in price of $17711.29, given that all variables are held constant.

Analysis of Variance:

Sum of squares df Mean square

Regression 868018 6 144670 Residual 766332 825 928.888 Total 1.63435e+006 831 1981.03

R^2 = 868018 / 1.63435e+006 = 0.531109
F(6, 825) = 144670 / 928.888 = 155.745 [p-value 5.04e-132]

Question 3:
Is the estimated effect of LOT on PRICE in the regression in part (2) very different from the regression in part (1)? Based on this, does the regression in part (1) seems to suffer from important omitted variable bias? What are the two conditions for omitted variable...
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