Introduction to Linear Algebra

Simple linear regression is useful for finding a relationship between two continuous variables. One is a predictor or independent variable and other is a response or dependent variable. It looks for a statistical relationship but not a deterministic relationship. The relationship between the two variables is said to be deterministic if one variable can be accurately expressed by the other. For example, using temperature in degree Celsius it is possible to accurately predict Fahrenheit. Statistical relationship is not accurate in determining the relationship between two variables. For example, the relationship between height and weight.

With simple linear regression we want to model our data as follows:
y = B0 + B1 * x
This is a line where y is the output variable we want to predict, x is the input variable we know and B0 and B1 are coefficients we need to estimate.

 It also required us to understand the concept of gradient descent. Gradient Descent is the process of minimizing a function by following the gradients of the cost function.
This involves knowing the form of the cost as well as the derivative so that from a given point you know the gradient and can move in that direction, e.g. downhill towards the minimum value.
After understanding the various concepts involved, we then started writing the numpy implementation of Linear Regression on a randomly created data.

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