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

  • Thread starter Thread starter zmalone
  • Start date Start date
  • Tags Tags
    Ols
Click For Summary
SUMMARY

The discussion focuses on calculating the Ordinary Least Squares (OLS) estimator for β1 given β0 = 3 and specific summations from a dataset of 50 points. The key equations involved include Σ(Yi - 3 - β1Xi)^2, which simplifies to a function of one unknown, β1. Participants emphasize using one-variable calculus to minimize this function and derive the estimator. The numerical values provided, such as ΣiYi = 500 and ΣiXiYi = 8000, are crucial for calculating the specific value of β1.

PREREQUISITES
  • Understanding of Ordinary Least Squares (OLS) regression
  • Familiarity with calculus, particularly one-variable optimization
  • Knowledge of statistical summation notation
  • Basic proficiency in interpreting regression coefficients
NEXT STEPS
  • Study the derivation of OLS estimators in detail
  • Learn how to apply one-variable calculus in optimization problems
  • Explore the implications of fixed β0 values in regression analysis
  • Review practical examples of OLS calculations using real datasets
USEFUL FOR

Students in statistics or econometrics, data analysts, and anyone interested in understanding the mechanics of OLS regression and its applications in data analysis.

zmalone
Messages
10
Reaction score
0

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!
 
Physics news on Phys.org
Your dispersion function
[tex] \sum {\left(Y_i - 3 - b_1 x_i\right)^2}[/tex]

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
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
6K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
Replies
5
Views
5K
  • · Replies 65 ·
3
Replies
65
Views
14K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K