Parameter Estimation with Backfitting (part 1/2): R illustration with two predictors

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[@whatever--]

really interesting, thanks for the video

[@statisticsmatt]

You're welcome. Many thanks for watching! Don't forget to subscribe and let others know about this channel.

[@wolpumba4099]

*Summary*
*Parameter Estimation with Backfitting (Part 1/2)*
* *Goal:* Estimate parameters in multiple linear regression using only simple linear regression.
* *Method:* Backfitting - an iterative process of estimating parameters one at a time while holding others fixed.
* *Steps:*
1. *Data Generation (**0:00**):* Create 100 data points with two predictors (X1, X2) and one response variable (Y).
2. *Initialization (**3:00**):* Make an initial guess for one parameter (e.g., beta 1).
3. *Iteration (**3:00**):*
* Use the fixed value of beta 1 to estimate beta 2 via simple linear regression.
* Fix beta 2 at its new estimate and re-estimate beta 1.
* Use both beta 1 and beta 2 to estimate the intercept (beta 0).
* Store these estimates and repeat the process for a set number of iterations (e.g., 50).
* *Convergence (**6:00**):* The estimates for beta 0, beta 1, and beta 2 converge to the least squares estimates from multiple linear regression after a few iterations.
* *Visualization (**8:42**):* The convergence of parameter estimates across iterations can be visualized using a plot.
* *Comparison (**9:30**):* The backfitting estimates are shown to be identical to those obtained from directly fitting a multiple linear regression model.
*Key takeaway:* Backfitting provides a way to estimate parameters in situations where only simple linear regression tools are available.
i used gemini 1.5 pro to summarize the transcript

[@statisticsmatt]

That's amazing. Many thanks, and many thanks for watching. Don't forget to subscribe and let others know about this channel.