BUS 215 Lecture 12: Derivation of OLS Estimators Notes

• School: Stony Brook University
• Department: Business Management
• Course: BUS 215
• Professor: Aaron Young- Shin Kim

Document Summary

Step 2: take first derivatives and equate to zero: (2) (4) Step 3: in (3) and (5) take sums and simplify to obtain (6) and (7): (6) (7) n i. Step 4: since xi and yi and n are known, we can use equations (6) and (7) for the two unknown values b0 and b1. And multiply (7) by n to get equations (8) and (9): 1 x i i (8) (9) n n i i y i. 1 n i x i n n i i x i. Step 5: subtract equation (9) from equation (8) to eliminate the middle term involving b0: (10) n n. Step 6: move the terms that do not involve b1 to the right-hand side: (11) b. 1 x i i i x nb i. 1 y i i i x n i n. 1 x i i i n x i n. 1 i x y i i n n x i.