How Do You Optimize a and b in Linear Regression for Minimal Deviation?

[oleandora]

Homework Statement

I've been given a set of data
x 0 0.5 0.7 1.5 1.75
y 0.5 0.72 0.51 1.5 1.63

Given y=ax+b

for this data points of linear model, I have to
1. minimize the sum of the absolute values of deviations between experimental value of Y and value predicted by the linear relation
2. minimiza the maximum value of deviation between all experimental values of Y and value predicted by linear relation

The question is
What are the optimal values of a and b for both cases and values of objective function.

Homework Equations

The Attempt at a Solution

What I know is
y=ax+b+e where e is the deviation but that's it. I don't even have the slightest idea for the next steps.
I know seems simplebut I have very little background on linear regression.
Help! T_T

 

[MaxManus]

Hey, this is the first time I tried to help someone on this forum, so don't shoot me if I am wronge. If we are at the same level I guess you are supposed to use OLS Ordinary Least Square.

b = $$\sum$$ (X_i-$$\bar{X}$$)(Y_i-$$\bar{Y}$$)/
$$\sum$$ (X_i-$$\bar{X}$$)²

a = $$\bar{Y}$$ - b$$\bar{X}$$

where you sum from 1 to n.
$$\bar{X}$$ means the average