## 
## Call:
## lm(formula = property_price_log ~ lot_land_area_log + living_area_ratio + 
##     price_per_living_area_unit_usd, data = zillowmorgantown)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.7531 -0.0795  0.1185  0.2926  0.5947 
## 
## Coefficients:
##                                  Estimate Std. Error t value
## (Intercept)                    10.7195287  0.3290716  32.575
## lot_land_area_log              -0.1169859  0.0317447  -3.685
## living_area_ratio               0.0411534  0.0036838  11.171
## price_per_living_area_unit_usd  0.0122438  0.0005841  20.962
##                                            Pr(>|t|)    
## (Intercept)                    < 0.0000000000000002 ***
## lot_land_area_log                          0.000274 ***
## living_area_ratio              < 0.0000000000000002 ***
## price_per_living_area_unit_usd < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5628 on 280 degrees of freedom
## Multiple R-squared:  0.6596, Adjusted R-squared:  0.656 
## F-statistic: 180.9 on 3 and 280 DF,  p-value: < 0.00000000000000022
## 
## Call:
## lm(formula = property_price_usd ~ living_area_ratio + price_per_living_area_unit_usd, 
##     data = zillowmorgantown)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -625107  -19653   -2110   27792  113073 
## 
## Coefficients:
##                                 Estimate Std. Error t value            Pr(>|t|)
## (Intercept)                    -111893.3    11850.6  -9.442 <0.0000000000000002
## living_area_ratio                 7538.5      373.6  20.178 <0.0000000000000002
## price_per_living_area_unit_usd    1424.1       59.6  23.893 <0.0000000000000002
##                                   
## (Intercept)                    ***
## living_area_ratio              ***
## price_per_living_area_unit_usd ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 57650 on 281 degrees of freedom
## Multiple R-squared:  0.7507, Adjusted R-squared:  0.7489 
## F-statistic:   423 on 2 and 281 DF,  p-value: < 0.00000000000000022
## 
## Call:
## lm(formula = property_price_usd ~ price_per_living_area_unit_usd + 
##     bedrooms + bathrooms, data = zillowmorgantown)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -400396  -35251    -210   36334  188033 
## 
## Coefficients:
##                                  Estimate Std. Error t value
## (Intercept)                    -106933.92   13673.78  -7.820
## price_per_living_area_unit_usd    1278.08      65.58  19.490
## bedrooms                         28840.72    3694.59   7.806
## bathrooms                        31951.03    4324.36   7.389
##                                            Pr(>|t|)    
## (Intercept)                       0.000000000000111 ***
## price_per_living_area_unit_usd < 0.0000000000000002 ***
## bedrooms                          0.000000000000122 ***
## bathrooms                         0.000000000001755 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 63300 on 277 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.6972, Adjusted R-squared:  0.6939 
## F-statistic: 212.6 on 3 and 277 DF,  p-value: < 0.00000000000000022

##                    lot_land_area_sqft property_price_usd   bedrooms
## lot_land_area_sqft          1.0000000         -0.2248229 -0.2551373
## property_price_usd         -0.2248229          1.0000000  0.4583067
## bedrooms                   -0.2551373          0.4583067  1.0000000

```

Both M and m2 yield better r^2 values than m3 although I think m3 is the best determinent for the cost of the house, despite what the data says. There are many ways to get to a high r^2 with this data, but I have not found one that yielded a logical result in terms of a positive price for a house as the intercept.