1. Introduction:
  1. There should be a Linear and Additive relationship between dependent (output: y) and independent (inputs: X’s) variables. The linear relationship creates a straight line when plotted on a graph. An additive relationship means that the effect of X’s on y is independent of other variables.
  2. There should be no correlation between the error or residual terms. The absence of this phenomenon is known as Autocorrelation.
  3. The independent (X’s) variables should not be correlated, the absence of phenomena is called multi-collinearity.
  4. The error term must have constant variance. The phenomenon is known as homoskedasticity. The presence of non-constant variance is referred to as heteroskedasticity.
  5. The error term must be normally distributed.
Linear Regression Hypothesis
Different hypotheses based on different values of θ’s
The cost function of Linear Regression
Gradient Descent Algorithm with m: training dataset size
Weight update
  • data: contains the information for various houses
  • target: prices of the house
  • feature_names: names of the features
  • DESCR: describes the dataset
boston.head()
Correlation matrix

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