Question

log type: smcl

opened on: 30 Jan 2019, 23:24:04

. 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 |

      +-----------------+

. log close

log type: smcl

closed on: 30 Jan 2019, 23:27:13

2. Written assignment

Answer the following questions:

a. Is the data used in this exercise time-series data or cross-section data?

b. Is the data used in this exercise micro data or macro data?

c. 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?

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

    Stata software (Do not copy and paste the regression output table from Stata).

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

     coefficient?

f.   Interpret the estimated slope coefficient.

g. 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?

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

Answer 1

Answer 2 (a) : The data used in this exercise is a cross-section data. As can be seen here, the cross-section data involves a statistical data or collected information from various subjects or platforms either in a definite point of time or time spreading in to various points. As can be seen here, the data involves data of price and its corresponding square feet where the price in accordance to the square feet measurement is not in a series of equivalent time intervals.

Answer 2 (b) : The Data used in this exercise is a micro level data. A micro data involves the statistical data of the individual sector firm or of a person or per sector data. We can see here that the data in this exercise shows us the price per square feet of data.

Answer 2 ( c) : The average sale price of a house in this sample is = Mean price / mean square feet

                                                                                                                      = 154863.2/ 2325.938

                                                                                                                       = $ 66.58

                         The average size of a house in this sample is given as 2325.938 square feet.

                         The estimated covariance between price and Sqft is 1.0e+06 whereas the estimated correlation coefficient is sqft 9.4e+07 against price 1.5e+10

                        The estimated covariance and correlation between the sale price and the size of a house suggests that the price in correlation to the size of the house is not in a risky state. This is because a positive covariant and correlation coefficient indicate that the price of the definitive size of the house is in positive state in the market and does not have risks.

                     

Answer 2 (h) : The estimated intercept coefficient is meaningful when the value of the constant x Is NIL or Zero (0) . In such a scenario, the intercept is only the mean or the average value of the coefficient. Therefore, here, the intercept coefficient does not hold too much of a meaning.