econ2P91_Assignment3_SOLUTIONS_Fall2009 - ECON 2P91...

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ECON 2P91: Business Econometrics with Applications Fall 2009 Assignment 3 (Due Date: Monday November 30th 2009) - SOLUTIONS In assignments1 and 2, you investigated the relationship between residential housing price and lot size by constructing hedonic price models for the City of Prince George, British Columbia, Canada. In this assignment, you will refine the previous models with a focus on the following questions. First, are there seasonal differences in residential housing prices? Second, is the relationship between lot size and price linear? As a by-product, you will examine the use of econometric models for estimating the means of variables and the associated confidence intervals. For this assignment, you will employ the data for 1011 residential houses sold in Prince George during the period from the first quarter of 2001 to the first quarter of 2002. As in the previous assignments, LOT denotes lot size (acres), PRICE is the residential housing price (thousands of dollars). We have added a binary variable D ( 1 = D if the house was sold in Spring/Summer and 0 = D otherwise). ID is the housing identification variable. The relevant data are provided in the Excel data file princegeorge_housing3.xls , which is available on Sakai. 1. Obtain the descriptive statistics of PRICE and interpret the values of the coefficient of skewness and the coefficient of excess kurtosis. Summary Statistics, using the observations 1 - 1011 for the variable 'price' (1011 valid observations) Mean 119.91 Median 117.00 Minimum 22.500 Maximum 385.00 Standard deviation 44.169 C.V. 0.36835 Skewness 1.1046 Ex. kurtosis 3.8509 Coefficient of skewness (1.1046) is positive indicating positive skewness i.e. long tail is in the positive direction. Excess kurtosis (3.8509) is positive, meaning that the coefficient of kurtosis is greater than 3, indicating that the distribution has a higher peak than the normal distribution. Note that excess kurtosis is equal to coefficient of kurtosis minus 3. In this case, the coefficient of kurtosis must be 3.8507+3=6.8507. 1
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2. Use the mean and standard deviation you obtained in part (1) to compute (by hand) a 95 percent confidence interval for the average price. 95 percent confidence interval = ) 1011 / 169 . 44 ( 96 . 1 91 . 119 ) / ( 96 . 1 ± = ± n s x x = 723 . 2 91 . 119 ± i.e. 117.187 to 122.633. 3. Run a regression of PRICE on a constant and compare the estimate of the constant with the estimate of the mean you obtained in part (1). On the basis of these results, what can you conclude about the effect of running a regression of any variable on a constant? Model 1: OLS estimates using the 1011 observations 1-1011 Dependent variable: price VARIABLE COEFFICIENT STDERROR T STAT P-VALUE const 119.911 1.38911 86.322 <0.00001 *** Mean of dependent variable = 119.911 Standard deviation of dep. var. = 44.1686 Sum of squared residuals = 1.97037e+006 Standard error of residuals = 44.1686 Unadjusted R-squared = 0.00000 Adjusted R-squared = 0.00000
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econ2P91_Assignment3_SOLUTIONS_Fall2009 - ECON 2P91...

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