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Simple Linear Regression

What is the causal effect of x on y ?

What is the predicted value of y for a given x ?

Example

New product on profits

user ratings on sales

2 ways to find causal effect

Experiments

  • Random Controlled Trials (RCTs)
  • A/B Testing

Observational Data

Example

Predict price of house for a given size

Predict sales for a given query and consumer characterstics

Forecasting : Special Case for predicting future values

  1. Visualise with Scatterplot

Direction

Curvature

Strength

  1. Quantifying Association

Measure for Linear association

Covariance

Correlation

Function : Cov(x, y) = E[(x − µx )(y − µy )]

Properties

Reflects Direction of relationship

Magnitude depends on scale of attributes

Function : Corr(x, y) = Cov(x, y)/(σxσy)

Properties

−1 ≤ Corr(X, Y ) ≤ 1

Corr(X,Y) = 1 ; strong, positive, linear