Linear Regression by Hand

Linear Regression by Hand

Explanation on how to model a linear regression by Hand and with Code for Python and R. Calculating Line Regression by Hand. When there are more than 2 points of data it is usually impossible to find a line that goes exactly through all the points.

The basic idea behind linear regression is quite simple. In mathematical terms we want to predict a dependent variable Y using an independent variable X. By assuming that the two variables correlate in a linear fashion we can predict Y with a simple linear formula:

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Linear equation by Author

(The wavy equal sign signifies “approximately”). Simply put, as soon as we know a bit about the relationship between the two coefficients, i.e. we have approximated the two coefficients α *and *β, we can (with some confidence) predict Y. Alpha α represents the intercept (value of y with f(x = 0)) and Beta β is the slope.

With the help of linear regression, we can answer a lot of questions; e.g.

  • “Is the rise of sea level connected to rising temperatures?”,
  • “How expensive will a house with 3 bedrooms be?”
  • “How many items do we sell if we increase our marketing budget by 20%?”

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