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Multiple Linear Regression
Correlations

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:

Positive and Negative Linear Relationships

Instructions

1.

Create a scatterplot of size_sqft and rent:

plt.scatter(df[['size_sqft']], df[['rent']], alpha=0.4)

Is there a strong correlation?

2.

Create a scatterplot of min_to_subway and rent:

plt.scatter(df[['min_to_subway']], df[['rent']], alpha=0.4)

Is there a strong correlation?

3.

Do the same for a few others and write down the ones that don’t have strong correlations.

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