We will have to find the equation that follows the form:
That is:
*The value of a is:
*The value of b is:
So, the linear regression is:
We can see it graphically as follows:
Here we can see the linear regression line and the points used.
***How to manually determine linear regressions***
We will start as follows:
We will have to use the following expressions in order to manually find the linear regression:
And:
Here we have that n is the number of values on the dataset. So, we solve for b as follows [Based on the problem given]:
*We will determine the values of n, the sum of x, the sum of y, xy, x^2 & y^2 as follows:
Sum of x:
Sum of y:
Value of n: We have that the number of datasets given is 6 [6 pairs of values on the table].
*The sum of xy:
*The sum of X^2:
*The square of the sum of x:
Now that we have all the values, we replace in the first equation and solve for b:
And we solve now for a:
And then we simply replace on the expression:
And the expression after the replacement of a & b is the linear regression.