The least-squares regression line is:
a. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.
b. the line that passes through the most data points.
c. All of the answer options are correct.
d. the line such that half of the data points fall above the line and half fall below the line.

a. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.

Step-by-step explanation:

If we have N points and we want to adjust a model

We can define the error associated to this like that:

So as we can see here we are adding the square distances between the real and the adjusted values in order to minimize the error for this reason the correct answer is:

a. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.

For this case we need to calculate the slope with the following formula:

Where:

And we can find the intercept using this:

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )