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gretl: model 1 File Edit Tests Save Graphs Analysis LaTeX Question 5 In your first year microeconomics course you learned about differentiated products. As an econometrics student differentiated products are interesting because they are prime candidates for hedonic price modelling. As mentioned in class, a hedonic price model is a regression model that relates the price of a differentiated product (a residential house in this case) to its characteristics. For this assignment you will construct a simple hedonic model for residential housing and estimate its parameters using real Canadian data. Model 1: OLS, using observations 1-832 Dependent variable: PRICE coefficient std. error t-ratio p-value const LOT 119.575 1.38850 1.54566 0.209083 77.36 6.641 0.0000 *** 5.63e-11 *** Mean dependent var Sum squared resid R-squared F(1, 830) Log-likelihood Schwarz criterion 122.0756 1551891 0.050454 44.10150 -4313.516 8640.480 S.D. dependent var S.E. of regression Adjusted R-squared P-value (F) Akaike criterion Hannan-Quinn 44.34779 43.24059 0.049309 5.63e-11 8631.033 8634.655 Do houses with bigger lot sizes sell for higher prices? To answer this question empirically, we will construct a simple hedonic price model for an unspecified Canadian city using real data on 832 residential houses that were sold in this city during a particular calendar year. These data are reported in the Excel data file hedonic.xls. For this hedonic data set, lot size (LOT ) is measured in acres and residential housing price PRICE) is measured in thousands of Canadian dollars; QUARTER denotes the quarter in which each house was sold (QUARTER=1 denotes the first quarter (Winter); QUARTER= 2 denotes the second quarter (Spring); QUARTER=3 denotes the third quarter (Summer); and QUARTER=4 denotes the fourth quarter (Fall)). The variable ID is the housing identification variable. gretl: ANOVA Analysis of Variance: (a) Use GRETL to obtain OLS estimates of the parameters of the model PRICE = B. +BLOT, +u, . Write the regression results in the standard format as discussed in class and also illustrated in the notes section below i.e. including R and SER with the estimated standard error recorded below each intercept and slope coefficient (b) For the estimated regression in Part (a), provide appropriate interpretations for the estimated intercept and slope parameters B, and ß , respectively. (c) Test, at 5% level of significance, the null hypothesis, H,: B = 0 against a one-sided alternative H,:B, >0. (d) Construct a 95% confidence interval for the intercept coefficient B.. What does the estimated confidence interval suggest about the significance of B.? (e) Interpret the value of the coefficient of determination RP. Note that only indicating "good fit” or “poor fit” does not constitute detailed explanation. (f) Use the estimated regression in Part 1 to predict the mean price of a residential house in this city with a lot size of 0.5 acres. (g) Use GRETL to construct an ANOVA table for the estimated regression in Part (a). What are the values of the Total Sum of Squares (TSS), Explained Sum of Squares (ESS), and Residual Sum of Squares (SSR) from the ANOVA table? Explain the meanings of these sums of squares. What is the relationship between the three sums of squares? Sum of squares df Mean square Regression Residual Total 82458.7 1.55189e+06 1.63435e+06 1 830 831 82458.7 1869.75 1966.73 R^2 = 82458.7 / 1.63435e+06 = 0.050454 F(1, 830) = 82458.7 / 1869.75 = 44.1015 [p-value 5.63e-11]

Answer 1

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Ans: a) from the giren output, the regression egh is Price - 119.575 +1.3885 Lot. (1.54566) (0.209083) R?= 0.050454 for every b) Interprestation of Lot one unit incuese en lat size, there is corresponding $1.3885 encuere en housing Price Interpretation of Intercept: If there is no change in lost size, the will be $119.575. ) Ho! B, 20 Hq 6, 20. it 6.641, pralve -0.000 since value 70.05 so reject Ho and ralue of cofficient af slop is positive house prie conclude the P it at d) 957 wsth 890 df = 1.96. 957 CI2 Bot AXS.E(Bo) 119.575 +1.96X1.546 5 (116-55, 122.61 if there is no change in lot size, we are 957. confident that the prie will lies en blo (116:55, I 124.61) CSscanned with CamScanner