Prior to discussing how to calculate least squares regression line let us define what a regression line is. A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes.

Ordinary least squares regression is a way to find the line of best fit for a set of data.

### Formula to Calculate Squares Regression Line.

Since the line’s equation is y = mx + b, all we need to do is find the values of m (gradient) and b (y-intercept) using the following formulas.

N is the number of points

x,y are the values on the x and y axis.

M is the gradient.

**Example:**

Suppose you found out how many hours of sunshine verse how many bottles of water were sold at the shop from Monday to Friday to be as follows;

Hours of Sunshine (x) | Bottles of Water Sold (y) |

6 | 12 |

5 | 10 |

4 | 8 |

5 | 7 |

5 | 9 |

Therefore, we will begin by finding the value of m.

We first need to find;

N = 5

Σx^2 = 625

Σy = 46

Σxy = 234

Σx = 25

Therefore m is;

m = 0.00833

Therefore, the y-intercept is 9.2.

If y = mx + b

Then y = 0.00833x + 9.2