How to Calculate OLS Estimator with Given β0 in 50 Data Points?

[zmalone]

Homework Statement

ΣiYi = 500; ΣiXi = 150; ΣiYi2 = 17000; ΣiXi2 = 4000; ΣiXiYi = 8000; n = 50.

β0 = 3. Derive formula for OLS estimator of β1 and find estimate

Homework Equations

I'm new to OLS and I'm not sure where to go from:

Σ(Yi - 3 - b1Xi)^2

I was able to walk through the steps in my class lectures to solve Bhat1 and Bhat0 but am a little confused when β0 is given. Can anyone explain the logical following steps? Thank you!

 

[statdad]

Your dispersion function
$$\sum {\left(Y_i - 3 - b_1 x_i\right)^2}$$

is now just a function of one unknown. Use methods of one-variable calculus to minimize it, then use the numerical information provided above to find the specific value

 

[EconomicTheory]

The following post explains exactly how the estimator is derived. You basically just have to plug in your variables. http://economictheoryblog.com/2015/02/19/ols_estimator/