Question

ECO 4421                           Assignment 1                      

Consider the following simple regression model of housing prices:

Price_i = β₁ + β₂Sqft_i + u_i

where,

Price = the sale price of a house (in $)

Sqft    = the size of a house (in square feet)

The file br2.dta contains data on the sales of 1080 houses sold in Louisiana during June 2005. The data include information on the sale price of a house, the square feet in the house, as well as other information about the property sold. This assignment uses data only for the Price and Sqft variables.

use "/Users/br2.dta"

. summarize price sqft

    Variable |        Obs        Mean    Std. Dev.       Min        Max

-------------+---------------------------------------------------------

       price |      1,080    154863.2    122912.8      22000    1580000

        sqft |      1,080    2325.938    1008.098        662       7897

. correlate price sqft

(obs=1,080)

             |    price     sqft

-------------+------------------

       price |   1.0000

        sqft |   0.7607   1.0000

. correlate price sqft, covariance

(obs=1,080)

             |    price     sqft

-------------+------------------

       price | 1.5e+10

        sqft | 9.4e+07 1.0e+06

. regress price sqft

      Source |       SS           df       MS      Number of obs   =     1,080

-------------+----------------------------------   F(1, 1078)      =   1480.43

       Model | 9.4326e+12         1 9.4326e+12   Prob > F        =    0.0000

    Residual | 6.8685e+12     1,078 6.3715e+09   R-squared       =    0.5786

-------------+----------------------------------   Adj R-squared   =    0.5783

       Total | 1.6301e+13     1,079 1.5108e+10   Root MSE        =     79822

------------------------------------------------------------------------------

       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

        sqft |   92.74737   2.410502    38.48   0.000     88.01757    97.47718

       _cons | -60861.46   6110.187    -9.96   0.000    -72850.67   -48872.25

------------------------------------------------------------------------------

. predict yhat

(option xb assumed; fitted values)

. set obs 1081

number of observations (_N) was 1,080, now 1,081

. replace sqft = 3800 in 1081

(1 real change made)

. predict yhat1

(option xb assumed; fitted values)

. list sqft yhat1 in 1081

      +-----------------+

      | sqft      yhat1 |

      |-----------------|

1081. | 3800   291578.6 |

      +-----------------+

2. Written assignment

Answer the following questions:

a. What is the average sale price of a house in the sample? What is the average size of a

     house in the sample? What are the estimated covariance and correlation coefficients

     between Price and Sqft? What do the covariance and correlation coefficients suggest

     about the relationship between the sale price of a house and its size?

b. Report (in equation format) the estimated regression obtained above by applying the

    Stata software.

c. What are the values of the estimated slope coefficient and the estimated intercept

     coefficient?

d.   Interpret the estimated slope coefficient.

e. Is the sign of the estimated slope coefficient consistent with your expectations about

    the relationship between the sale price of a house and its size?

f. Is the estimated intercept coefficient a meaningful estimate? Why or why not?

Answer 1