Machine Learning 101 – Equation for a Line and Regression Line

Let’s go back to the regression problem we solved in Lecture 4. We are given a dataset.  You need to find the relationship between the two variables.

The record is given below:

Spending (x) Profit (t)
40 90
50 110
60 130
70 150
80 170
120 250

Note that we’ve removed the year column. I have also modified the data.

Also, we would call the Spendings column, x and the Profit column y.

Here we can represent this table as:

x = {40, 50, 60, 70, 80, 120}

t = {90, 110, 130, 250, 170, 240}

We read this as:

x is a column vector made up of 6 elements. This can be written also as:

x = {x1, x2, . . . , xn}T where N = 6

Similarly, for y, we have

t = {t1, t2, . . . , tN}T where N = 6


Our goal is to used this data set (training data) to make prediction. So if we have a new value of x, let’s say xi, what would be the corresponding ti.

One way to achieve this is to use a method called curve fitting(or polynomial curve fitting).

Before we discuss curve fitting, let’s review Equation of a Line.


Review of Equation for a Line

If you did some mathematics, then you will remember that every line has an equation.

The equation for a line has the general form:

y = mx + c or

y  = c + mx


m is the slope of the line and

c is the intercept of the line on the y axis

This is the generic relationship between x and y that can be plotted on a straight line

This is illustrated in the figure below.

Equation of a straight line

This means that the relationship between the two variables is given by the equation of the line.

So if we can find the values of m and c, then we just plug it into the equation.

Now let’s rewrite this equation in a more Machine Learning way

y = ß0 + ß1x

This then means that regression is simply a problem of finding ß0 and ß1 which we call the regression coefficient


Practical: Using Python to find Regression Coefficients

Let’s do a little practical. We would find the regression coefficients of using Python.

The Jupyter Notebook screenshot is given below:

Linear Regression for Machine Learning 101 Lecture 5


In the next Lecture, we would continue with Polynomial Curve Equation.



Kindson Munonye is currently completing his doctoral program in Software Engineering in Budapest University of Technology and Economics

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