In our Manhattan model, we used 14 variables, so there are 14 coefficients:

[ -302.73009383  1199.3859951  4.79976742 
 -24.28993151  24.19824177 -7.58272473  
-140.90664773  48.85017415 191.4257324  
-151.11453388  89.408889  -57.89714551  
-19.31948556  -38.92369828 ]

• bedrooms - number of bedrooms
• bathrooms - number of bathrooms
• size_sqft - size in square feet
• min_to_subway - distance from subway station in minutes
• floor - floor number
• building_age_yrs - building’s age in years
• no_fee - has no broker fee (0 for fee, 1 for no fee)
• has_roofdeck - has roof deck (0 for no, 1 for yes)
• has_washer_dryer - has in-unit washer/dryer (0/1)
• has_doorman - has doorman (0/1)
• has_elevator - has elevator (0/1)
• has_dishwasher - has dishwasher (0/1)
• has_patio - has patio (0/1)
• has_gym - has gym (0/1)

To see if there are any features that don’t affect price linearly, let’s graph the different features against rent.

Interpreting graphs

In regression, the independent variables will either have a positive linear relationship to the dependent variable, a negative linear relationship, or no relationship. A negative linear relationship means that as X values increase, Y values will decrease. Similarly, a positive linear relationship means that as X values increase, Y values will also increase.

Graphically, when you see a downward trend, it means a negative linear relationship exists. When you find an upward trend, it indicates a positive linear relationship. Here are two graphs indicating positive and negative linear relationships: