Question

A problem of interest is the relationship between the appraised value of a property and its sale price. The sale price for any given property will vary depending on the price set by the seller, the strength of appeal of the property to a specific buyer, and the state of the money and real estate markets. We want to examine the relationship between the mean sale price E(y) of a property and the variables: appraised land value of the property, appraised value of the improvements on the property and neighborhood in which the property is listed. The data were collected from the property appraiser’s office of Hillsborough County, Florida, and saved in the TAMSALES4 file. Four neighborhoods (Hyde Park, Cheval, Hunter’s Green, and Davis Isles), each relatively homogeneous but differing sociologically and in property types and values, were identified within the city and surrounding area.

1. Draw scatter plots between the response Y and the quantitative variables.

2. Using the information, you got from the scatter plot and the knowledge in chapter 4 and 5, propose at least 3 different model to find the relation between the mean sale price E(y) and the variables. Try to build the models in such a way that one is nested in other.

3. Conduct partial F test repeatedly and find a best model from the proposed models.

4. After the final model has been selected, Conduct the Global F test for the adequacy of the model.

5. Perform individual t test if you have doubt with any one of the variables.

6. Report the value of adjusted R-squared and standard error of the model.

7. Depending on your report in step six, explain in your word if the final model is good to use or it may need some improvements.

8. Provide all the R codes you have used. TAMSALES4 file:

Using Rstudio:

FOLIO   SALES   LNSALES   LAND   IMP   TOTVAL   NBHD
129295710   378.0   5.93489   81.84   243.30   325.14   CHEVAL
129295830   273.0   5.60947   60.48   134.47   194.95   CHEVAL
129453028   321.2   5.77206   115.58   255.42   371.00   CHEVAL
129454156   327.0   5.78996   112.38   185.57   297.96   CHEVAL
129454194   382.5   5.94673   81.23   217.98   299.22   CHEVAL
129454316   242.0   5.48894   61.48   110.28   171.76   CHEVAL
129454374   242.0   5.48894   49.99   109.06   159.06   CHEVAL
129454524   510.0   6.23441   71.28   224.38   295.65   CHEVAL
129454536   285.0   5.65249   63.82   158.83   222.65   CHEVAL
129795122   500.0   6.21461   91.32   296.02   387.34   CHEVAL
129795276   825.0   6.71538   117.01   451.41   568.42   CHEVAL
129795456   515.0   6.24417   117.72   347.87   465.59   CHEVAL
129795468   520.0   6.25383   107.06   329.93   436.99   CHEVAL
129795488   780.0   6.65929   157.29   507.85   665.14   CHEVAL
129795506   825.0   6.71538   131.89   466.27   598.16   CHEVAL
129795510   841.0   6.73459   159.84   443.29   603.13   CHEVAL
129795606   1140.0   7.03878   157.49   563.91   721.41   CHEVAL
129842052   460.0   6.13123   59.36   206.84   266.20   CHEVAL
339720192   285.0   5.65249   39.75   166.61   206.36   HUNTERSGREEN
339721514   350.0   5.85793   54.00   227.43   281.43   HUNTERSGREEN
339721560   314.5   5.75098   48.84   187.13   235.97   HUNTERSGREEN
594030716   183.0   5.20949   34.75   158.05   192.80   HUNTERSGREEN
594030754   200.0   5.29832   29.10   145.80   174.90   HUNTERSGREEN
594030784   775.0   6.65286   142.27   350.43   492.70   HUNTERSGREEN
594030788   505.0   6.22456   99.62   306.43   406.05   HUNTERSGREEN
594030880   425.0   6.05209   47.52   225.74   273.26   HUNTERSGREEN
594030882   335.0   5.81413   49.01   217.35   266.36   HUNTERSGREEN
594031020   760.0   6.63332   96.10   335.59   431.69   HUNTERSGREEN
594031044   410.0   6.01616   75.79   274.22   350.01   HUNTERSGREEN
594031064   335.0   5.81413   67.22   273.66   340.88   HUNTERSGREEN
594033934   325.0   5.78383   47.02   241.87   288.90   HUNTERSGREEN
594033956   380.0   5.94017   47.74   307.20   354.94   HUNTERSGREEN
594033970   640.0   6.46147   45.55   336.44   381.99   HUNTERSGREEN
594034072   262.0   5.56834   51.97   152.96   204.94   HUNTERSGREEN
594034084   190.0   5.24702   51.25   151.68   202.94   HUNTERSGREEN
1176450000   500.0   6.21461   256.13   152.78   408.91   HYDEPARK
1186250000   550.0   6.30992   168.45   310.12   478.56   HYDEPARK
1186260000   205.8   5.32690   168.45   41.60   210.05   HYDEPARK
1692460000   590.0   6.38012   291.09   66.90   357.99   DAVISISLES
1692730000   525.0   6.26340   462.43   114.13   576.56   DAVISISLES
1692990000   340.0   5.82895   199.66   80.43   280.09   DAVISISLES
1693500000   3200.0   8.07091   1004.59   1129.65   2134.23   DAVISISLES
1694120000   500.0   6.21461   358.43   55.89   414.32   DAVISISLES
1694450000   1421.0   7.25912   391.46   550.78   942.24   DAVISISLES
1853130000   858.9   6.75565   242.47   281.62   524.09   HYDEPARK
1853270000   625.0   6.43775   264.00   184.63   448.63   HYDEPARK
1854060000   375.0   5.92693   242.00   33.79   275.79   HYDEPARK
1854250000   1240.0   7.12287   264.00   466.82   730.82   HYDEPARK
1855080000   850.0   6.74524   266.64   333.18   599.82   HYDEPARK
1855250000   2500.0   7.82405   533.28   1221.20   1754.48   HYDEPARK
1855590000   750.0   6.62007   266.64   366.05   632.69   HYDEPARK
1856430000   895.0   6.79682   266.64   358.77   625.41   HYDEPARK
1856800000   460.0   6.13123   264.00   183.54   447.54   HYDEPARK
1856960000   605.0   6.40523   210.00   259.67   469.67   HYDEPARK
1857420000   329.9   5.79879   210.00   105.94   315.94   HYDEPARK
1857460000   462.0   6.13556   210.00   145.19   355.19   HYDEPARK
1858190000   850.0   6.74524   264.00   362.71   626.71   HYDEPARK
1858440000   1525.0   7.32975   335.61   862.34   1197.95   HYDEPARK
1858450000   1400.0   7.24423   350.90   711.34   1062.24   HYDEPARK
1858770000   760.0   6.63332   264.00   257.47   521.47   HYDEPARK
1859190000   520.0   6.25383   250.23   157.75   407.98   HYDEPARK
1859400000   418.0   6.03548   193.20   147.43   340.63   HYDEPARK
1859590000   152.0   5.02388   118.80   106.14   224.94   HYDEPARK
1859620000   330.0   5.79909   118.80   123.98   242.78   HYDEPARK
1860510000   240.0   5.48064   192.01   221.54   413.55   HYDEPARK
1860580000   405.0   6.00389   223.74   122.18   345.92   HYDEPARK
1860890000   650.0   6.47697   203.49   209.11   412.60   HYDEPARK
1860920000   400.0   5.99146   203.49   101.58   305.07   HYDEPARK
1861000000   365.0   5.89990   207.48   112.78   320.26   HYDEPARK
1953960000   745.0   6.61338   291.63   83.22   374.85   DAVISISLES
1954130000   1650.0   7.40853   388.82   1023.36   1412.18   DAVISISLES
1954320000   1250.0   7.13090   648.96   81.01   729.97   DAVISISLES
1954870000   715.0   6.57228   344.12   265.18   609.30   DAVISISLES
1955990000   1215.0   7.10250   341.86   785.66   1127.52   DAVISISLES
1960100000   440.0   6.08677   179.52   58.40   237.92   DAVISISLES
1962380000   690.0   6.53669   357.07   121.25   478.33   DAVISISLES
1964590000   587.5   6.37588   300.93   75.99   376.92   DAVISISLES
1966620000   377.5   5.93357   238.86   43.95   282.81   DAVISISLES
1968140000   810.0   6.69703   195.84   479.00   674.84   DAVISISLES
1969380000   800.0   6.68461   242.47   367.40   609.87   HYDEPARK

Answer 1

Here Model 4 highly significant because p value is less than 0.05.