Linear Regression -- Everything you need to know

Whenever we talk about Linear Regression we always talk about finding the best fit line for the data, well, That exactly is the objective of Linear Regression, but there's more to it than just fitting the line, So let's talk about why and how we find this best fit line. As the name suggests, the algorithm works on data that follows a linear trend, thus if we can find a line that could correctly define the trend of the data, we can very likely use the same line to define the whole dataset, thus using the same line, we can even get the values at points that are not present in the dataset, this is called prediction. Take a look at the dataset below, it is pretty clear that it does follow a linear trend. So just by looking at the dataset can we find what will be the output at any point, Yes we can, But real-world data is not this easy to interpret just by looking at it, in these cases we can rely on the underlying Mathematics of the Algorithm to find the line that could find and understand the trend in the data and adapt to it. Let's take the data shown in figure 1.